User contributions
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- 07:54, 26 December 2023 (diff | hist) . . (+2) . . 1997 OIM Problems/Problem 6 (→Problem) (current)
- 19:29, 23 December 2023 (diff | hist) . . (-5) . . 1997 OIM Problems/Problem 4 (→Problem) (current)
- 10:29, 23 December 2023 (diff | hist) . . (+65) . . 1996 OIM Problems/Problem 1 (current)
- 10:27, 23 December 2023 (diff | hist) . . (+820) . . 1996 OIM Problems/Problem 1
- 10:11, 23 December 2023 (diff | hist) . . (-2) . . 1996 OIM Problems/Problem 1
- 10:10, 23 December 2023 (diff | hist) . . (+258) . . 1996 OIM Problems/Problem 1
- 09:58, 23 December 2023 (diff | hist) . . (+718) . . 1996 OIM Problems/Problem 1
- 09:43, 23 December 2023 (diff | hist) . . (+32) . . 1992 OIM Problems/Problem 1 (→See also) (current)
- 09:42, 23 December 2023 (diff | hist) . . (+32) . . 1992 OIM Problems/Problem 2 (→See also) (current)
- 09:42, 23 December 2023 (diff | hist) . . (+32) . . 1992 OIM Problems/Problem 3 (→See also) (current)
- 09:42, 23 December 2023 (diff | hist) . . (+32) . . 1992 OIM Problems/Problem 4 (→See also) (current)
- 09:42, 23 December 2023 (diff | hist) . . (+32) . . 1992 OIM Problems/Problem 5 (→See also) (current)
- 09:41, 23 December 2023 (diff | hist) . . (+32) . . 1992 OIM Problems/Problem 6 (→See also) (current)
- 09:41, 23 December 2023 (diff | hist) . . (+32) . . 1991 OIM Problems/Problem 6 (→See also) (current)
- 09:41, 23 December 2023 (diff | hist) . . (+32) . . 1991 OIM Problems/Problem 5 (→See also) (current)
- 09:40, 23 December 2023 (diff | hist) . . (+1) . . 1991 OIM Problems/Problem 3 (→See also) (current)
- 09:40, 23 December 2023 (diff | hist) . . (+1) . . 1991 OIM Problems/Problem 2 (→See also) (current)
- 09:40, 23 December 2023 (diff | hist) . . (+1) . . 1991 OIM Problems/Problem 1 (→See also) (current)
- 09:40, 23 December 2023 (diff | hist) . . (+2) . . 1991 OIM Problems/Problem 4 (→See also) (current)
- 09:39, 23 December 2023 (diff | hist) . . (+31) . . 1991 OIM Problems/Problem 4 (→See also)
- 09:39, 23 December 2023 (diff | hist) . . (+31) . . 1991 OIM Problems/Problem 3
- 09:39, 23 December 2023 (diff | hist) . . (+31) . . 1991 OIM Problems/Problem 2
- 09:38, 23 December 2023 (diff | hist) . . (+31) . . 1991 OIM Problems/Problem 1
- 09:38, 23 December 2023 (diff | hist) . . (-2) . . 2020 OIM Problems/Problem 3 (current)
- 09:24, 23 December 2023 (diff | hist) . . (0) . . 1992 OIM Problems/Problem 2
- 01:50, 23 December 2023 (diff | hist) . . (0) . . 1985 OIM Problems/Problem 5 (current)
- 01:50, 23 December 2023 (diff | hist) . . (+70) . . 1985 OIM Problems/Problem 5
- 01:49, 23 December 2023 (diff | hist) . . (+369) . . 1985 OIM Problems/Problem 5
- 01:22, 23 December 2023 (diff | hist) . . (-1) . . 1990 OIM Problems/Problem 3 (current)
- 01:21, 23 December 2023 (diff | hist) . . (+511) . . 1990 OIM Problems/Problem 1 (current)
- 01:14, 23 December 2023 (diff | hist) . . (+430) . . 1990 OIM Problems/Problem 1
- 00:51, 23 December 2023 (diff | hist) . . (+2) . . 1990 OIM Problems/Problem 1
- 00:48, 23 December 2023 (diff | hist) . . (+37) . . 1992 OIM Problems/Problem 4
- 00:47, 23 December 2023 (diff | hist) . . (+37) . . 1992 OIM Problems/Problem 2
- 00:46, 23 December 2023 (diff | hist) . . (+36) . . 1991 OIM Problems/Problem 5
- 00:46, 23 December 2023 (diff | hist) . . (+36) . . 1991 OIM Problems/Problem 6
- 00:45, 23 December 2023 (diff | hist) . . (+705) . . 1991 OIM Problems/Problem 2
- 00:40, 23 December 2023 (diff | hist) . . (+624) . . 1991 OIM Problems/Problem 2
- 00:35, 23 December 2023 (diff | hist) . . (+13) . . 1991 OIM Problems/Problem 2
- 00:34, 23 December 2023 (diff | hist) . . (+263) . . 1991 OIM Problems/Problem 2
- 00:30, 23 December 2023 (diff | hist) . . (+12) . . 1991 OIM Problems/Problem 2
- 00:29, 23 December 2023 (diff | hist) . . (+172) . . 1991 OIM Problems/Problem 2
- 00:26, 23 December 2023 (diff | hist) . . (+184) . . 1991 OIM Problems/Problem 2
- 00:24, 23 December 2023 (diff | hist) . . (0) . . 1991 OIM Problems/Problem 2
- 00:23, 23 December 2023 (diff | hist) . . (+51) . . 1991 OIM Problems/Problem 2
- 00:20, 23 December 2023 (diff | hist) . . (+121) . . 1991 OIM Problems/Problem 2
- 00:17, 23 December 2023 (diff | hist) . . (0) . . N File:1991 OIM p2c.png (current)
- 00:17, 23 December 2023 (diff | hist) . . (0) . . 1991 OIM Problems/Problem 2
- 00:15, 23 December 2023 (diff | hist) . . (0) . . 1991 OIM Problems/Problem 2
- 00:15, 23 December 2023 (diff | hist) . . (0) . . 1991 OIM Problems/Problem 2
- 00:15, 23 December 2023 (diff | hist) . . (+6) . . 1991 OIM Problems/Problem 2
- 00:14, 23 December 2023 (diff | hist) . . (0) . . N File:1991 OIM p2b.png (current)
- 00:13, 23 December 2023 (diff | hist) . . (0) . . N File:1991 OIM p2a.png (current)
- 00:12, 23 December 2023 (diff | hist) . . (+75) . . 1991 OIM Problems/Problem 2
- 22:09, 22 December 2023 (diff | hist) . . (+17) . . 1991 OIM Problems/Problem 2 (→Solution)
- 22:05, 22 December 2023 (diff | hist) . . (+15) . . 1991 OIM Problems/Problem 5
- 22:04, 22 December 2023 (diff | hist) . . (+66) . . 1991 OIM Problems/Problem 5
- 22:03, 22 December 2023 (diff | hist) . . (+620) . . 1991 OIM Problems/Problem 5
- 22:03, 22 December 2023 (diff | hist) . . (-620) . . 1991 OIM Problems/Problem 5
- 22:02, 22 December 2023 (diff | hist) . . (+620) . . 1991 OIM Problems/Problem 5
- 21:34, 22 December 2023 (diff | hist) . . (+737) . . 1991 OIM Problems/Problem 5
- 21:28, 22 December 2023 (diff | hist) . . (+2,376) . . 1991 OIM Problems/Problem 5
- 21:25, 22 December 2023 (diff | hist) . . (+380) . . 1991 OIM Problems/Problem 5
- 21:23, 22 December 2023 (diff | hist) . . (-36) . . 1991 OIM Problems/Problem 5
- 21:23, 22 December 2023 (diff | hist) . . (+65) . . 1991 OIM Problems/Problem 5
- 21:21, 22 December 2023 (diff | hist) . . (+2,161) . . 1991 OIM Problems/Problem 5
- 21:11, 22 December 2023 (diff | hist) . . (0) . . 1991 OIM Problems/Problem 5
- 21:10, 22 December 2023 (diff | hist) . . (+249) . . 1991 OIM Problems/Problem 5
- 21:08, 22 December 2023 (diff | hist) . . (+293) . . 1991 OIM Problems/Problem 5
- 21:05, 22 December 2023 (diff | hist) . . (+245) . . 1991 OIM Problems/Problem 5
- 21:01, 22 December 2023 (diff | hist) . . (+104) . . 1991 OIM Problems/Problem 5
- 20:59, 22 December 2023 (diff | hist) . . (+389) . . 1991 OIM Problems/Problem 5
- 19:45, 22 December 2023 (diff | hist) . . (0) . . N File:1991 OIM P6d.png (current)
- 19:45, 22 December 2023 (diff | hist) . . (0) . . N File:1991 OIM P6c.png (current)
- 19:44, 22 December 2023 (diff | hist) . . (+2,120) . . 1991 OIM Problems/Problem 6
- 19:21, 22 December 2023 (diff | hist) . . (+1,024) . . 1991 OIM Problems/Problem 6
- 19:11, 22 December 2023 (diff | hist) . . (0) . . N File:1991 OIM P6b.png (current)
- 19:10, 22 December 2023 (diff | hist) . . (+13) . . 1991 OIM Problems/Problem 6
- 19:10, 22 December 2023 (diff | hist) . . (+823) . . 1991 OIM Problems/Problem 6
- 19:04, 22 December 2023 (diff | hist) . . (0) . . N File:1991 OIM P6a.png (current)
- 19:03, 22 December 2023 (diff | hist) . . (+112) . . 1991 OIM Problems/Problem 6
- 19:03, 22 December 2023 (diff | hist) . . (+44) . . 1991 OIM Problems/Problem 6
- 19:01, 22 December 2023 (diff | hist) . . (+14) . . 1991 OIM Problems/Problem 6
- 14:56, 22 December 2023 (diff | hist) . . (0) . . 1992 OIM Problems/Problem 2
- 14:55, 22 December 2023 (diff | hist) . . (0) . . 1992 OIM Problems/Problem 2
- 14:54, 22 December 2023 (diff | hist) . . (0) . . 1992 OIM Problems/Problem 2
- 13:35, 20 December 2023 (diff | hist) . . (+1) . . 1992 OIM Problems/Problem 4
- 13:17, 20 December 2023 (diff | hist) . . (+35) . . 1992 OIM Problems/Problem 6
- 13:07, 20 December 2023 (diff | hist) . . (+36) . . 1992 OIM Problems/Problem 6
- 13:06, 20 December 2023 (diff | hist) . . (-3) . . 1992 OIM Problems/Problem 6
- 13:03, 20 December 2023 (diff | hist) . . (+634) . . 1992 OIM Problems/Problem 6
- 12:50, 20 December 2023 (diff | hist) . . (+10) . . 1992 OIM Problems/Problem 6
- 12:46, 20 December 2023 (diff | hist) . . (+128) . . 1992 OIM Problems/Problem 6
- 12:38, 20 December 2023 (diff | hist) . . (+165) . . 1992 OIM Problems/Problem 6
- 12:35, 20 December 2023 (diff | hist) . . (+69) . . 1992 OIM Problems/Problem 6
- 12:35, 20 December 2023 (diff | hist) . . (+196) . . 1992 OIM Problems/Problem 6
- 12:20, 20 December 2023 (diff | hist) . . (+182) . . 1992 OIM Problems/Problem 6
- 12:07, 20 December 2023 (diff | hist) . . (+57) . . 1992 OIM Problems/Problem 6
- 11:39, 20 December 2023 (diff | hist) . . (+136) . . 1992 OIM Problems/Problem 6
- 11:36, 20 December 2023 (diff | hist) . . (+92) . . 1992 OIM Problems/Problem 6
- 11:05, 20 December 2023 (diff | hist) . . (-1) . . 1992 OIM Problems/Problem 6
- 11:04, 20 December 2023 (diff | hist) . . (+1) . . 1992 OIM Problems/Problem 6
- 11:04, 20 December 2023 (diff | hist) . . (+798) . . 1992 OIM Problems/Problem 6
- 01:14, 20 December 2023 (diff | hist) . . (+35) . . 1992 OIM Problems/Problem 5
- 01:14, 20 December 2023 (diff | hist) . . (0) . . 1992 OIM Problems/Problem 5
- 01:12, 20 December 2023 (diff | hist) . . (-17) . . 1992 OIM Problems/Problem 5
- 01:11, 20 December 2023 (diff | hist) . . (+12) . . 1992 OIM Problems/Problem 5
- 01:09, 20 December 2023 (diff | hist) . . (+755) . . 1992 OIM Problems/Problem 5
- 01:01, 20 December 2023 (diff | hist) . . (0) . . N File:1992 OIM P5c.png (current)
- 01:00, 20 December 2023 (diff | hist) . . (+6) . . 1992 OIM Problems/Problem 5
- 01:00, 20 December 2023 (diff | hist) . . (+1) . . 1992 OIM Problems/Problem 5
- 00:59, 20 December 2023 (diff | hist) . . (0) . . N File:1992 OIM P5e.png (current)
- 00:59, 20 December 2023 (diff | hist) . . (+325) . . 1992 OIM Problems/Problem 5
- 00:55, 20 December 2023 (diff | hist) . . (0) . . N File:1992 OIM P5d.png (current)
- 00:55, 20 December 2023 (diff | hist) . . (+440) . . 1992 OIM Problems/Problem 5
- 00:49, 20 December 2023 (diff | hist) . . (+627) . . 1992 OIM Problems/Problem 5
- 00:45, 20 December 2023 (diff | hist) . . (0) . . N File:1992 OIM P5b.png (current)
- 00:42, 20 December 2023 (diff | hist) . . (+468) . . 1992 OIM Problems/Problem 5
- 00:38, 20 December 2023 (diff | hist) . . (0) . . N File:1992 OIM P5a.png (current)
- 21:35, 19 December 2023 (diff | hist) . . (+44) . . 1992 OIM Problems/Problem 3
- 21:34, 19 December 2023 (diff | hist) . . (+59) . . 1992 OIM Problems/Problem 2
- 21:32, 19 December 2023 (diff | hist) . . (+84) . . 1992 OIM Problems/Problem 4
- 21:29, 19 December 2023 (diff | hist) . . (+55) . . 1992 OIM Problems/Problem 4
- 21:28, 19 December 2023 (diff | hist) . . (0) . . 1992 OIM Problems/Problem 4
- 21:27, 19 December 2023 (diff | hist) . . (+76) . . 1992 OIM Problems/Problem 4
- 21:25, 19 December 2023 (diff | hist) . . (+80) . . 1992 OIM Problems/Problem 4
- 21:24, 19 December 2023 (diff | hist) . . (+28) . . 1992 OIM Problems/Problem 4
- 21:23, 19 December 2023 (diff | hist) . . (+384) . . 1992 OIM Problems/Problem 4
- 21:19, 19 December 2023 (diff | hist) . . (+41) . . 1992 OIM Problems/Problem 4
- 21:17, 19 December 2023 (diff | hist) . . (+105) . . 1992 OIM Problems/Problem 4
- 21:16, 19 December 2023 (diff | hist) . . (+316) . . 1992 OIM Problems/Problem 4
- 21:10, 19 December 2023 (diff | hist) . . (-13) . . 1992 OIM Problems/Problem 4
- 12:58, 17 December 2023 (diff | hist) . . (+2) . . 1992 OIM Problems/Problem 2
- 12:39, 17 December 2023 (diff | hist) . . (+118) . . 1992 OIM Problems/Problem 2
- 12:38, 17 December 2023 (diff | hist) . . (+85) . . 1992 OIM Problems/Problem 2
- 12:36, 17 December 2023 (diff | hist) . . (+99) . . 1992 OIM Problems/Problem 2
- 12:35, 17 December 2023 (diff | hist) . . (+1) . . 1992 OIM Problems/Problem 2
- 12:34, 17 December 2023 (diff | hist) . . (+45) . . 1992 OIM Problems/Problem 2
- 12:33, 17 December 2023 (diff | hist) . . (+238) . . 1992 OIM Problems/Problem 2
- 12:32, 17 December 2023 (diff | hist) . . (+4) . . 1992 OIM Problems/Problem 2
- 12:31, 17 December 2023 (diff | hist) . . (+301) . . 1992 OIM Problems/Problem 2
- 12:29, 17 December 2023 (diff | hist) . . (+154) . . 1992 OIM Problems/Problem 2
- 12:13, 17 December 2023 (diff | hist) . . (-1) . . 1992 OIM Problems/Problem 2
- 12:11, 17 December 2023 (diff | hist) . . (+301) . . 1992 OIM Problems/Problem 2
- 12:07, 17 December 2023 (diff | hist) . . (0) . . 1992 OIM Problems/Problem 2
- 12:07, 17 December 2023 (diff | hist) . . (0) . . 1992 OIM Problems/Problem 2
- 12:06, 17 December 2023 (diff | hist) . . (0) . . N File:1992 OIM P2b.png (current)
- 12:02, 17 December 2023 (diff | hist) . . (0) . . 1992 OIM Problems/Problem 2
- 12:01, 17 December 2023 (diff | hist) . . (+311) . . 1992 OIM Problems/Problem 2
- 11:57, 17 December 2023 (diff | hist) . . (+1) . . 1992 OIM Problems/Problem 2
- 11:57, 17 December 2023 (diff | hist) . . (0) . . N File:1992 OIM P2a.png (current)
- 11:55, 17 December 2023 (diff | hist) . . (0) . . 1992 OIM Problems/Problem 2
- 11:55, 17 December 2023 (diff | hist) . . (+50) . . 1992 OIM Problems/Problem 2
- 11:54, 17 December 2023 (diff | hist) . . (0) . . N File:1992 OIM P2.png (current)
- 11:34, 17 December 2023 (diff | hist) . . (+3) . . 1992 OIM Problems/Problem 2
- 11:25, 15 December 2023 (diff | hist) . . (-72) . . 1992 OIM Problems/Problem 1
- 11:22, 15 December 2023 (diff | hist) . . (+67) . . 1992 OIM Problems/Problem 1
- 11:22, 15 December 2023 (diff | hist) . . (+105) . . 1992 OIM Problems/Problem 1
- 11:19, 15 December 2023 (diff | hist) . . (+1) . . 1992 OIM Problems/Problem 1
- 22:26, 14 December 2023 (diff | hist) . . (-2) . . 1992 OIM Problems/Problem 6 (→Solution)
- 22:20, 14 December 2023 (diff | hist) . . (+1,322) . . 1992 OIM Problems/Problem 3
- 22:02, 14 December 2023 (diff | hist) . . (+254) . . 1992 OIM Problems/Problem 3
- 21:59, 14 December 2023 (diff | hist) . . (+343) . . 1992 OIM Problems/Problem 3
- 21:54, 14 December 2023 (diff | hist) . . (+102) . . 1992 OIM Problems/Problem 3
- 21:53, 14 December 2023 (diff | hist) . . (+280) . . 1992 OIM Problems/Problem 3
- 21:49, 14 December 2023 (diff | hist) . . (+285) . . 1992 OIM Problems/Problem 3
- 21:47, 14 December 2023 (diff | hist) . . (+165) . . 1992 OIM Problems/Problem 3
- 21:44, 14 December 2023 (diff | hist) . . (-61) . . 1992 OIM Problems/Problem 3
- 21:43, 14 December 2023 (diff | hist) . . (+177) . . 1992 OIM Problems/Problem 3
- 21:42, 14 December 2023 (diff | hist) . . (+377) . . 1992 OIM Problems/Problem 3
- 21:35, 14 December 2023 (diff | hist) . . (+242) . . 1992 OIM Problems/Problem 3
- 21:32, 14 December 2023 (diff | hist) . . (0) . . 1992 OIM Problems/Problem 3
- 21:32, 14 December 2023 (diff | hist) . . (+40) . . 1992 OIM Problems/Problem 3
- 21:31, 14 December 2023 (diff | hist) . . (0) . . N File:1992 OIM P3.png (current)
- 18:28, 14 December 2023 (diff | hist) . . (+198) . . 1991 OIM Problems/Problem 6
- 18:27, 14 December 2023 (diff | hist) . . (+182) . . 1991 OIM Problems/Problem 5
- 18:26, 14 December 2023 (diff | hist) . . (+189) . . 1991 OIM Problems/Problem 2
- 18:25, 14 December 2023 (diff | hist) . . (+210) . . 1992 OIM Problems/Problem 6
- 18:24, 14 December 2023 (diff | hist) . . (+464) . . 1992 OIM Problems/Problem 5
- 18:21, 14 December 2023 (diff | hist) . . (+219) . . 1992 OIM Problems/Problem 4
- 18:21, 14 December 2023 (diff | hist) . . (+45) . . 1992 OIM Problems/Problem 2
- 18:20, 14 December 2023 (diff | hist) . . (+253) . . 1992 OIM Problems/Problem 3
- 18:18, 14 December 2023 (diff | hist) . . (+337) . . 1992 OIM Problems/Problem 2
- 18:03, 14 December 2023 (diff | hist) . . (+468) . . N XXXVIII Olimpiada Iberoamericana de Matemáticas (OIM) (Created page with "XXXVIII Olimpiada Iberoamericana de Matemáticas was held in Río de Janeiro, Brasil , 2023 * Problem 1 * 2023 OIM Problems/Problem 2...") (current)
- 18:03, 14 December 2023 (diff | hist) . . (+461) . . N XXXVII Olimpiada Iberoamericana de Matemáticas (OIM) (Created page with "XXXVII Olimpiada Iberoamericana de Matemáticas was held in Bogotá, Colombia , 2022 * Problem 1 * 2022 OIM Problems/Problem 2 | Prob...") (current)
- 18:03, 14 December 2023 (diff | hist) . . (+462) . . N XXXVI Olimpiada Iberoamericana de Matemáticas (OIM) (Created page with "XXXVI Olimpiada Iberoamericana de Matemáticas was held in on-line, Costa Rica , 2021 * Problem 1 * 2021 OIM Problems/Problem 2 | Pro...") (current)
- 18:02, 14 December 2023 (diff | hist) . . (+456) . . N XXXV Olimpiada Iberoamericana de Matemáticas (OIM) (Created page with "XXXV Olimpiada Iberoamericana de Matemáticas was held in on-line, Perú , 2020 * Problem 1 * 2020 OIM Problems/Problem 2 | Problem 2...") (current)
- 18:02, 14 December 2023 (diff | hist) . . (+462) . . N XXXIV Olimpiada Iberoamericana de Matemáticas (OIM) (Created page with "XXXIV Olimpiada Iberoamericana de Matemáticas was held in Guanajuato, México , 2019 * Problem 1 * 2019 OIM Problems/Problem 2 | Pro...") (current)
- 18:02, 14 December 2023 (diff | hist) . . (+471) . . N XXXIII Olimpiada Iberoamericana de Matemáticas (OIM) (Created page with "XXXIII Olimpiada Iberoamericana de Matemáticas was held in La Rábida, España-Portugal, 2018 * Problem 1 * 2018 OIM Problems/Proble...") (current)
- 18:01, 14 December 2023 (diff | hist) . . (+468) . . N XXXII Olimpiada Iberoamericana de Matemáticas (OIM) (Created page with "XXXII Olimpiada Iberoamericana de Matemáticas was held in Puerto Iguazú, Argentina , 2017 * Problem 1 * 2017 OIM Problems/Problem 2...") (current)
- 18:01, 14 December 2023 (diff | hist) . . (+447) . . N XXXI Olimpiada Iberoamericana de Matemáticas (OIM) (Created page with "XXXI Olimpiada Iberoamericana de Matemáticas was held in Chile , 2016 * Problem 1 * Problem 2 * 2...") (current)
- 18:01, 14 December 2023 (diff | hist) . . (+463) . . N XXX Olimpiada Iberoamericana de Matemáticas (OIM) (Created page with "XXX Olimpiada Iberoamericana de Matemáticas was held in Mayagüez, Puerto Rico , 2015 * Problem 1 * 2015 OIM Problems/Problem 2 | Pr...") (current)
- 18:01, 14 December 2023 (diff | hist) . . (+466) . . N XXIX Olimpiada Iberoamericana de Matemáticas (OIM) (Created page with "XXIX Olimpiada Iberoamericana de Matemáticas was held in San Pedro Sula, Honduras , 2014 * Problem 1 * 2014 OIM Problems/Problem 2 |...") (current)
- 18:00, 14 December 2023 (diff | hist) . . (+461) . . N XXVIII Olimpiada Iberoamericana de Matemáticas (OIM) (Created page with "XXVIII Olimpiada Iberoamericana de Matemáticas was held in Ciudad de Panamá , 2013 * Problem 1 * 2013 OIM Problems/Problem 2 | Prob...") (current)
- 18:00, 14 December 2023 (diff | hist) . . (+462) . . N XXVII Olimpiada Iberoamericana de Matemáticas (OIM) (Created page with "XXVII Olimpiada Iberoamericana de Matemáticas was held in Cochabamba, Bolivia , 2012 * Problem 1 * 2012 OIM Problems/Problem 2 | Pro...") (current)
- 18:00, 14 December 2023 (diff | hist) . . (+466) . . N XXVI Olimpiada Iberoamericana de Matemáticas (OIM) (Created page with "XXVI Olimpiada Iberoamericana de Matemáticas was held in San José de Costa Rica, , 2011 * Problem 1 * 2011 OIM Problems/Problem 2 |...") (current)
- 18:00, 14 December 2023 (diff | hist) . . (+460) . . N XXV Olimpiada Iberoamericana de Matemáticas (OIM) (Created page with "XXV Olimpiada Iberoamericana de Matemáticas was held in Asunción, Paraguay , 2010 * Problem 1 * 2010 OIM Problems/Problem 2 | Probl...") (current)
- 17:59, 14 December 2023 (diff | hist) . . (+473) . . N XXIV Olimpiada Iberoamericana de Matemáticas (OIM) (Created page with "XXIV Olimpiada Iberoamericana de Matemáticas was held in Santiago de Querétaro, México , 2009 * Problem 1 * 2009 OIM Problems/Prob...") (current)
- 17:59, 14 December 2023 (diff | hist) . . (+469) . . N XXIII Olimpiada Iberoamericana de Matemáticas (OIM) (Created page with "XXIII Olimpiada Iberoamericana de Matemáticas was held in Salvador de Bahía, Brasil , 2008 * Problem 1 * 2008 OIM Problems/Problem...") (current)
- 17:58, 14 December 2023 (diff | hist) . . (+459) . . N XXII Olimpiada Iberoamericana de Matemáticas (OIM) (Created page with "XXII Olimpiada Iberoamericana de Matemáticas was held in Coimbra, Portugal , 2007 * Problem 1 * 2007 OIM Problems/Problem 2 | Proble...") (current)
- 17:58, 14 December 2023 (diff | hist) . . (+459) . . N XXI Olimpiada Iberoamericana de Matemáticas (OIM) (Created page with "XXI Olimpiada Iberoamericana de Matemáticas was held in Guayaquil, Ecuador , 2006 * Problem 1 * 2006 OIM Problems/Problem 2 | Proble...") (current)
- 17:57, 14 December 2023 (diff | hist) . . (+469) . . N XX Olimpiada Iberoamericana de Matemáticas (OIM) (Created page with "XX Olimpiada Iberoamericana de Matemáticas was held in Cartagena de Indias, Colombia , 2005 * Problem 1 * 2005 OIM Problems/Problem...") (current)
- 17:57, 14 December 2023 (diff | hist) . . (+460) . . N XIX Olimpiada Iberoamericana de Matemáticas (OIM) (Created page with "XIX Olimpiada Iberoamericana de Matemáticas was held in Castellón, España , 2004 * Problem 1 * 2004 OIM Problems/Problem 2 | Probl...") (current)
- 17:57, 14 December 2023 (diff | hist) . . (+467) . . N XVIII Olimpiada Iberoamericana de Matemáticas (OIM) (Created page with "XVIII Olimpiada Iberoamericana de Matemáticas was held in Mar del Plata, Argentina , 2003 * Problem 1 * 2003 OIM Problems/Problem 2...") (current)
- 17:56, 14 December 2023 (diff | hist) . . (+467) . . N XVII Olimpiada Iberoamericana de Matemáticas (OIM) (Created page with "XVII Olimpiada Iberoamericana de Matemáticas was held in San Salvador, El Salvador , 2002 * Problem 1 * 2002 OIM Problems/Problem 2...") (current)
- 17:56, 14 December 2023 (diff | hist) . . (+455) . . N XVI Olimpiada Iberoamericana de Matemáticas (OIM) (Created page with "XVI Olimpiada Iberoamericana de Matemáticas was held in Minas, Uruguay , 2001 * Problem 1 * [[2001 OIM Problems/Problem 2 | Problem 2]...") (current)
- 17:56, 14 December 2023 (diff | hist) . . (+458) . . N XV Olimpiada Iberoamericana de Matemáticas (OIM) (Created page with "XV Olimpiada Iberoamericana de Matemáticas was held in Caracas, Venezuela , 2000 * Problem 1 * 2000 OIM Problems/Problem 2 | Problem...") (current)
- 17:54, 14 December 2023 (diff | hist) . . (+456) . . N XIV Olimpiada Iberoamericana de Matemáticas (OIM) (Created page with "XIV Olimpiada Iberoamericana de Matemáticas was held in La Habana, Cuba , 1999 * Problem 1 * 1999 OIM Problems/Problem 2 | Problem 2...") (current)
- 17:54, 14 December 2023 (diff | hist) . . (+469) . . N XIII Olimpiada Iberoamericana de Matemáticas (OIM) (Created page with "XIII Olimpiada Iberoamericana de Matemáticas was held in Puerto Plata, R. Dominicana , 1998 * Problem 1 * 1998 OIM Problems/Problem...") (current)
- 17:54, 14 December 2023 (diff | hist) . . (+461) . . N XII Olimpiada Iberoamericana de Matemáticas (OIM) (Created page with "XII Olimpiada Iberoamericana de Matemáticas was held in Guadalajara, México , 1997 * Problem 1 * 1997 OIM Problems/Problem 2 | Prob...") (current)
- 17:53, 14 December 2023 (diff | hist) . . (+463) . . N XI Olimpiada Iberoamericana de Matemáticas (OIM) (Created page with "XI Olimpiada Iberoamericana de Matemáticas was held in San José de Costa Rica , 1996 * Problem 1 * 1996 OIM Problems/Problem 2 | Pr...") (current)
- 17:53, 14 December 2023 (diff | hist) . . (+455) . . N X Olimpiada Iberoamericana de Matemáticas (OIM) (Created page with "X Olimpiada Iberoamericana de Matemáticas was held in Región V, Chile , 1995 * Problem 1 * [[1995 OIM Problems/Problem 2 | Problem 2]...") (current)
- 17:53, 14 December 2023 (diff | hist) . . (+457) . . N IX Olimpiada Iberoamericana de Matemáticas (OIM) (Created page with "IX Olimpiada Iberoamericana de Matemáticas was held in Fortaleza, Brasil , 1994 * Problem 1 * 1994 OIM Problems/Problem 2 | Problem...") (current)
- 17:52, 14 December 2023 (diff | hist) . . (+467) . . N VIII Olimpiada Iberoamericana de Matemáticas (OIM) (Created page with "VIII Olimpiada Iberoamericana de Matemáticas was held in Ciudad de México, México, 1993 * Problem 1 * 1993 OIM Problems/Problem 2...") (current)
- 17:52, 14 December 2023 (diff | hist) . . (+459) . . N VII Olimpiada Iberoamericana de Matemáticas (OIM) (Created page with "VII Olimpiada Iberoamericana de Matemáticas was held in Caracas, venezuela , 1992 * Problem 1 * 1992 OIM Problems/Problem 2 | Proble...") (current)
- 17:52, 14 December 2023 (diff | hist) . . (+459) . . N VI Olimpiada Iberoamericana de Matemáticas (OIM) (Created page with "VI Olimpiada Iberoamericana de Matemáticas was held in Córdoba, Argentina , 1991 * Problem 1 * 1991 OIM Problems/Problem 2 | Proble...") (current)
- 17:51, 14 December 2023 (diff | hist) . . (+458) . . N V Olimpiada Iberoamericana de Matemáticas (OIM) (Created page with "V Olimpiada Iberoamericana de Matemáticas was held in Valladolid, España , 1990 * Problem 1 * 1990 OIM Problems/Problem 2 | Problem...") (current)
- 17:51, 14 December 2023 (diff | hist) . . (+455) . . N IV Olimpiada Iberoamericana de Matemáticas (OIM) (Created page with "IV Olimpiada Iberoamericana de Matemáticas was held in La Habana, Cuba , 1989 * Problem 1 * [[1989 OIM Problems/Problem 2 | Problem 2]...") (current)
- 17:51, 14 December 2023 (diff | hist) . . (+452) . . N III Olimpiada Iberoamericana de Matemáticas (OIM) (Created page with "III Olimpiada Iberoamericana de Matemáticas was held in Lima, Perú , 1988 * Problem 1 * Problem 2...") (current)
- 17:50, 14 December 2023 (diff | hist) . . (+454) . . N II Olimpiada Iberoamericana de Matemáticas (OIM) (Created page with "II Olimpiada Iberoamericana de Matemáticas was held in Salto, Uruguay , 1987 * Problem 1 * Problem 2...") (current)
- 17:43, 14 December 2023 (diff | hist) . . (+10) . . I Olimpiada Iberoamericana de Matemáticas (OIM) (current)
- 17:42, 14 December 2023 (diff | hist) . . (+37) . . I Olimpiada Iberoamericana de Matemáticas (OIM)
- 17:41, 14 December 2023 (diff | hist) . . (0) . . I Olimpiada Iberoamericana de Matemáticas (OIM)
- 17:41, 14 December 2023 (diff | hist) . . (0) . . I Olimpiada Iberoamericana de Matemáticas (OIM)
- 17:41, 14 December 2023 (diff | hist) . . (-33) . . I Olimpiada Iberoamericana de Matemáticas (OIM)
- 17:40, 14 December 2023 (diff | hist) . . (+429) . . N I Olimpiada Iberoamericana de Matemáticas (OIM) (Created page with "The 7th OIM occurred in 1985 Colobia. * Problems * Problem 1 * Problem 2 * 1985 OIM...")
- 17:36, 14 December 2023 (diff | hist) . . (-2) . . 2004 OIM Problems/Problem 6 (current)
- 17:35, 14 December 2023 (diff | hist) . . (+906) . . N 2004 OIM Problems/Problem 6 (Created page with "== Problem == For a set <math>H</math> of points in the plane, a point <math>P</math> in the plane is said to be a point of intersection of <math>H</math> if there are four di...")
- 17:32, 14 December 2023 (diff | hist) . . (+798) . . N 2004 OIM Problems/Problem 5 (Created page with "== Problem == Given a scalene triangle <math>ABC</math>, Let <math>A', B'</math> and <math>C'</math> the points of intersection of the interior bisectors of angles <math>A, B<...") (current)
- 17:28, 14 December 2023 (diff | hist) . . (+360) . . N 2004 OIM Problems/Problem 4 (Created page with "== Problem == Find all pairs <math>(a, b)</math>, where <math>a</math> and <math>b</math> are positive integers of two digits each, such that <math>100a + b</math> and <math>2...") (current)
- 17:27, 14 December 2023 (diff | hist) . . (+424) . . N 2004 OIM Problems/Problem 3 (Created page with "== Problem == Let <math>n</math> and <math>k</math> be positive integers such that either <math>n</math> is odd or <math>n</math> and <math>k</math> are even. Prove that there...") (current)
- 17:26, 14 December 2023 (diff | hist) . . (+545) . . N 2004 OIM Problems/Problem 2 (Created page with "== Problem == A circle with center <math>O</math> and radius <math>r</math> are considered in the plane and a point <math>A</math> is considered outside of it. Let <math>M</ma...") (current)
- 17:24, 14 December 2023 (diff | hist) . . (+507) . . N 2004 OIM Problems/Problem 1 (Created page with "== Problem == Squares on a <math>1001 \times 1001</math> board must be colored according to the following rules: * If two squares have a common side, then at least one of the...") (current)
- 17:22, 14 December 2023 (diff | hist) . . (+13) . . 2005 OIM Problems/Problem 6
- 17:22, 14 December 2023 (diff | hist) . . (+787) . . N 2005 OIM Problems/Problem 6 (Created page with "== Problem == Given a positive integer <math>n</math>, <math>2n</math> points are aligned in a plane as <math>A_1, A_2,\cdots, A_{2n}. Each point is colored blue or red using...")
- 17:19, 14 December 2023 (diff | hist) . . (+666) . . N 2005 OIM Problems/Problem 5 (Created page with "== Problem == Let <math>O</math> be the circumcenter of an acute triangle <math>ABC</math> and <math>A_1</math> be a point on the smallest arc <math>BC</math> of the circumcir...") (current)
- 17:17, 14 December 2023 (diff | hist) . . (+560) . . N 2005 OIM Problems/Problem 4 (Created page with "== Problem == Given two positive integers <math>a</math> and <math>b</math>, <math>a\nabla b</math> denotes the remainder obtained by dividing <math>a</math> by <math>b</math>...") (current)
- 17:15, 14 December 2023 (diff | hist) . . (+432) . . N 2005 OIM Problems/Problem 3 (Created page with "== Problem == Let <math>p</math> greater than 3 be a prime number. If <cmath>\frac{1}{1^p}+\frac{1}{2^p}+\frac{1}{3^p}+\cdots+\frac{1}{(p-1)^p}=\frac{n}{m}</cmath> where th...") (current)
- 17:13, 14 December 2023 (diff | hist) . . (+782) . . N 2005 OIM Problems/Problem 2 (Created page with "== Problem == A flea jumps over integer points on the number line. In its first movement it jumps from point 0 and ands at point 1. Then, if in one movement the flea jumped fr...") (current)
- 17:10, 14 December 2023 (diff | hist) . . (+363) . . N 2005 OIM Problems/Problem 1 (Created page with "== Problem == Determine all triples of real numbers <math>(x, y, z)</math> that satisfy the following system of equations: <cmath>xyz = 8</cmath> <cmath>x^2y+y^2z+z^2x=73</cm...") (current)
- 17:08, 14 December 2023 (diff | hist) . . (-4) . . 2006 OIM Problems/Problem 6 (current)
- 17:08, 14 December 2023 (diff | hist) . . (+622) . . N 2006 OIM Problems/Problem 6 (Created page with "== Problem == Let <math>n > 1</math> be an odd integer. Let <math>P_0</math> and <math>P_1</math> be two consecutive vertices of a regular polygon with <math>n</math> sides. F...")
- 17:06, 14 December 2023 (diff | hist) . . (+628) . . N 2006 OIM Problems/Problem 5 (Created page with "== Problem == Given a circle <math>\Gamma</math>, consider a quadrilateral <math>ABCD</math> with its four sides tangent to <math>\Gamma</math>, with <math>AD</math> tangent t...") (current)
- 17:04, 14 December 2023 (diff | hist) . . (+335) . . N 2006 OIM Problems/Problem 4 (Created page with "== Problem == Find all pairs <math>(a, b)</math> of positive integers such that <math>2a + 1</math> and <math>2b - 1</math> are relative primes and <math>a + b</math> divides...") (current)
- 17:03, 14 December 2023 (diff | hist) . . (+1,019) . . N 2006 OIM Problems/Problem 3 (Created page with "== Problem == The numbers <math>1, 2, 3,\cdots , n^2</math> are placed in the squares of an <math>n \times n</math> grid, in some order, one number per box. A game piece is in...") (current)
- 17:00, 14 December 2023 (diff | hist) . . (+581) . . N 2006 OIM Problems/Problem 2 (Created page with "== Problem == We consider <math>n</math> real numbers <math>a_1, a_2,\cdots a_n</math> that are not necessarily different. Let <math>d</math> be the difference between the lar...") (current)
- 16:56, 14 December 2023 (diff | hist) . . (+750) . . N 2006 OIM Problems/Problem 1 (Created page with "== Problem == In the scalene triangle <math>ABC</math>, with <math>\angle BAC = 90^{\circ}</math>, the inscribed and circumscribed circles are considered. The tangent line at...") (current)
- 16:53, 14 December 2023 (diff | hist) . . (+11) . . 2007 OIM Problems/Problem 6 (current)
- 16:53, 14 December 2023 (diff | hist) . . (+687) . . N 2007 OIM Problems/Problem 6 (Created page with "== Problem == Let <math>F</math> be the family of all convex hexagons <math>H</math> such that the opposite sides of <math>H</math> are parallel, and any three vertices of <ma...")
- 16:51, 14 December 2023 (diff | hist) . . (-1) . . 2007 OIM Problems/Problem 5 (current)
- 16:51, 14 December 2023 (diff | hist) . . (+444) . . N 2007 OIM Problems/Problem 5 (Created page with "== Problem == A natural number <math>n</math> is "''daring''"<math> if the set of its divisors, from 1 to </math>n$ inclusive, can be divided into three subsets such that the...")
- 16:49, 14 December 2023 (diff | hist) . . (+1,015) . . N 2007 OIM Problems/Problem 4 (Created page with "== Problem == On a <math>19 \times 19</math> grid board, a piece called a "''dragon''" jumps from side to side in the following way: it moves 4 squares in a direction parallel...") (current)
- 16:46, 14 December 2023 (diff | hist) . . (+11) . . 2007 OIM Problems/Problem 3 (current)
- 16:46, 14 December 2023 (diff | hist) . . (+1,245) . . N 2007 OIM Problems/Problem 3 (Created page with "== Problem == Two teams, <math>A4 and </math>B<math>, dispute the territory limited by a circle. </math>A<math> has </math>n<math> blue flags and </math>B<math> has </math>n<m...")
- 16:43, 14 December 2023 (diff | hist) . . (+994) . . N 2007 OIM Problems/Problem 2 (Created page with "== Problem == Let <math>ABC</math> be a triangle with incenter <math>I</math> and <math>\Gamma</math> be a circle with center <math>I</math>, of radius greater than that of th...") (current)
- 16:40, 14 December 2023 (diff | hist) . . (+1) . . 2007 OIM Problems/Problem 1 (current)
- 16:40, 14 December 2023 (diff | hist) . . (+462) . . N 2007 OIM Problems/Problem 1 (Created page with "== Problem == Given a positive integer <math>m</math>, the sequence {<math>a_n</math>} is defined as follows: <math></math>a_1=\frac{m}{2},\;a_{n+1}=a_n\left\lceil a_n \right...")
- 16:37, 14 December 2023 (diff | hist) . . (+565) . . N 2008 OIM Problems/Problem 6 (Created page with "== Problem == In a "''biribol''" match, two teams of four people each face each other. A ''biribol'' tournament is organized in which <math>n</math> people participate, who f...") (current)
- 16:35, 14 December 2023 (diff | hist) . . (+717) . . N 2008 OIM Problems/Problem 5 (Created page with "== Problem == Let <math>ABC</math> be a triangle, and <math>X, Y, Z</math> be points on the sides <math>BC</math>, <math>AC</math>, <math>AB</math> respectively. Let <math>A'<...") (current)
- 16:32, 14 December 2023 (diff | hist) . . (0) . . 2008 OIM Problems/Problem 4 (current)
- 16:32, 14 December 2023 (diff | hist) . . (+274) . . N 2008 OIM Problems/Problem 4 (Created page with "== Problem == Prove that there are no positive integers <math>x</math> and <math>y</math> such that <cmath>s^{2008}+2008!=21^y</cmath> ~translated into English by Tomas Diaz...")
- 16:31, 14 December 2023 (diff | hist) . . (-2) . . 2008 OIM Problems/Problem 3 (current)
- 16:31, 14 December 2023 (diff | hist) . . (+453) . . N 2008 OIM Problems/Problem 3 (Created page with "== Problem == Let <math>m</math> and <math>n</math> be integers such that the polynomial <math>P(x) = x^3 + mx + n</math> has the following property: if <math>x</math> and <ma...")
- 16:30, 14 December 2023 (diff | hist) . . (+678) . . N 2008 OIM Problems/Problem 2 (Created page with "== Problem == Let <math>ABC</math> be a scalene triangle and <math>r</math> be the external bisector of the angle <math>\angle ABC</math>. <math>P</math> and <math>Q</math> ar...") (current)
- 16:28, 14 December 2023 (diff | hist) . . (+546) . . N 2008 OIM Problems/Problem 1 (Created page with "== Problem == Numbers <math>1, 2, 3, \cdots , 2008^2</math> were distributed on a <math>2008 \times 2008</math> board, such that in each box there is a different number. For e...") (current)
- 16:25, 14 December 2023 (diff | hist) . . (+495) . . N 2009 OIM Problems/Problem 6 (Created page with "== Problem == Around a circle, 6000 points are marked and each one is colored with one of 10 given colors, such that among any 100 consecutive points the 10 colors always appe...") (current)
- 16:24, 14 December 2023 (diff | hist) . . (+12) . . 2009 OIM Problems/Problem 5 (current)
- 16:24, 14 December 2023 (diff | hist) . . (+390) . . N 2009 OIM Problems/Problem 5 (Created page with "== Problem == The sequence <math>a_n</math> is defined by <math>a_1 = 1, a_{2k} = 1 + a_k</math>, and <math>a_{2k+1} = \frac{1}{a_{2k}}, for all integer </math>k \ge 1$. Prov...")
- 16:22, 14 December 2023 (diff | hist) . . (+677) . . N 2009 OIM Problems/Problem 4 (Created page with "== Problem == Let <math>ABC</math> be a triangle with <math>AB \ne AC</math>. Let <math>I</math> be the incenter of <math>ABC</math> and <math>P</math> the other point of inte...")
- 16:21, 14 December 2023 (diff | hist) . . (0) . . 2009 OIM Problems/Problem 3 (current)
- 16:21, 14 December 2023 (diff | hist) . . (-3) . . 2009 OIM Problems/Problem 3
- 16:20, 14 December 2023 (diff | hist) . . (+962) . . N 2009 OIM Problems/Problem 3 (Created page with "== Problem == Let <math>C_1</math> and <math>C_2</math> be two circles with centers <math>O_1</math> and <math>O_2</math> with the same radius, which intersect at <math>A</mat...")
- 16:17, 14 December 2023 (diff | hist) . . (+391) . . N 2009 OIM Problems/Problem 2 (Created page with "== Problem == For each positive integer <math>n</math> we define <math>a_n = n + m</math> where <math>m</math> is the largest integer such that <math>2^{2^m} \le n2^n</math>....") (current)
- 16:16, 14 December 2023 (diff | hist) . . (+558) . . N 2009 OIM Problems/Problem 1 (Created page with "== Problem == Let <math>n</math> be a natural number greater than 2. Suppose that <math>n</math> islands are located in a circle and that between each two neighboring islands...") (current)
- 16:14, 14 December 2023 (diff | hist) . . (+367) . . N 2010 OIM Problems/Problem 6 (Created page with "== Problem == 12 people sit around a circular table on which there are 28 vases. Two people can see each other if and only if there is no vase aligned with them. Prove that th...") (current)
- 16:13, 14 December 2023 (diff | hist) . . (+697) . . N 2010 OIM Problems/Problem 5 (Created page with "== Problem == Let <math>ABCD</math> be a cyclic quadrilateral whose diagonals <math>AC</math> and <math>BD</math> are perpendicular. Let <math>O</math> be the circumcenter of...") (current)
- 16:12, 14 December 2023 (diff | hist) . . (+12) . . 2010 OIM Problems/Problem 4 (current)
- 16:11, 14 December 2023 (diff | hist) . . (+523) . . N 2010 OIM Problems/Problem 4 (Created page with "== Problem == The arithmetic, geometric and harmonic means of two different positive integers are integer numbers. Find the smallest possible value for the arithmetic mean. '...")
- 16:09, 14 December 2023 (diff | hist) . . (+1,088) . . N 2010 OIM Problems/Problem 3 (Created page with "== Problem == The circle <math>\Gamma</math> inscribed in the scalene triangle <math>ABC</math> is tangent to the sides <math>BC</math>, <math>CA</math> and <math>AB</math> at...") (current)
- 16:07, 14 December 2023 (diff | hist) . . (+379) . . N 2010 OIM Problems/Problem 2 (Created page with "== Problem == Find if there are positive integers <math>a</math> and <math>b</math> such that all terms of the sequence defined by <cmath>x_1 = 2010,\; x_2 = 2011,\;x_{n+2}=...") (current)
- 16:04, 14 December 2023 (diff | hist) . . (+525) . . N 2010 OIM Problems/Problem 1 (Created page with "== Problem == There are ten indistinguishable coins placed in a line. It is known that two of them are false and occupy consecutive positions on the line. For each set of posi...") (current)
- 16:02, 14 December 2023 (diff | hist) . . (+721) . . N 2011 OIM Problems/Problem 6 (Created page with "== Problem == Let <math>k</math> and <math>n</math> be positive integers, with <math>k \ge 2</math>. In a straight line there are <math>kn</math> stones of <math>k</math> diff...") (current)
- 16:00, 14 December 2023 (diff | hist) . . (0) . . 2011 OIM Problems/Problem 5 (current)
- 15:58, 14 December 2023 (diff | hist) . . (+1) . . 2011 OIM Problems/Problem 5
- 15:57, 14 December 2023 (diff | hist) . . (+372) . . N 2011 OIM Problems/Problem 5 (Created page with "== Problem == Let <math>x_1, \cdots , x_n</math> be positive real numbers. Prove that there exist <math>a1, \cdots , a_n \in \left\{−1, 1\right\}</math> such that <cmath>a_...")
- 15:55, 14 December 2023 (diff | hist) . . (+439) . . N 2011 OIM Problems/Problem 4 (Created page with "== Problem == Let <math>ABC</math> be an acute triangle, with <math>AC \ne BC</math>, and let <math>O</math> be its circumcenter. Let <math>P</math> and <math>Q</math> points...") (current)
- 15:54, 14 December 2023 (diff | hist) . . (+1,081) . . N 2011 OIM Problems/Problem 3 (Created page with "== Problem == Let <math>ABC</math> be a triangle and let <math>X, Y, Z</math> be the points of tangency of its circumference inscribed with sides <math>BC</math>, <math>CA</ma...") (current)
- 15:51, 14 December 2023 (diff | hist) . . (+1) . . 2011 OIM Problems/Problem 2 (current)
- 15:51, 14 December 2023 (diff | hist) . . (+342) . . N 2011 OIM Problems/Problem 2 (Created page with "== Problem == Find all positive integers <math>n</math> for which there are three non-zero integers <math>x, y, z</math> such that <cmath>x+y+z=0,\;\frac{1}{x}+\frac{1}{y}\fr...")
- 15:50, 14 December 2023 (diff | hist) . . (+555) . . N 2011 OIM Problems/Problem 1 (Created page with "== Problem == The number 2 is written on the board. Ana and Bruno play alternately, starting with Ana. Each one in turn replaces the written number with the one obtained by ap...") (current)
- 15:48, 14 December 2023 (diff | hist) . . (+324) . . N 2012 OIM Problems/Problem 6 (Created page with "== Problem == Prove that for every positive integer <math>n</math> there are <math>n</math> consecutive positive integers such that none of them is divisible by the sum of the...") (current)
- 15:48, 14 December 2023 (diff | hist) . . (+647) . . N 2012 OIM Problems/Problem 5 (Created page with "== Problem == Let <math>ABC</math> be a triangle and let <math>P</math> and <math>Q</math> be the points of intersection of the parallel to <math>BC</math> by <math>A</math> w...") (current)
- 15:46, 14 December 2023 (diff | hist) . . (+415) . . N 2012 OIM Problems/Problem 4 (Created page with "== Problem == Let <math>a, b, c, d</math> be positive integers such that <math>a - b + c - d</math> is odd and divides <math>a^2 - b^2 + c^2 - d^2</math>. Show that <math>a -...") (current)
- 15:44, 14 December 2023 (diff | hist) . . (+701) . . N 2012 OIM Problems/Problem 3 (Created page with "== Problem == Let <math>n</math> be a positive integer. Given a set <math>\left\{a_1, a_2, \cdots , a_n\right\}</math> of integers between 0 and <math>2^n-1</math> inclusive,...") (current)
- 15:41, 14 December 2023 (diff | hist) . . (+472) . . N 2012 OIM Problems/Problem 2 (Created page with "== Problem == A positive integer is ''bisummed'' if it can be written as the sum of two integers positive numbers that have the same sum of their digits. For example, 2012 is...") (current)
- 15:39, 14 December 2023 (diff | hist) . . (+511) . . N 2012 OIM Problems/Problem 1 (Created page with "== Problem == Equilateral triangles <math>BCX</math> and <math>DCY</math> are drawn on a rectangle <math>ABCD</math> so that each one shares points with the interior of the re...") (current)
- 15:37, 14 December 2023 (diff | hist) . . (+549) . . N 2013 OIM Problems/Problem 6 (Created page with "== Problem == A ''configuration'' is a finite set <math>S</math> of points in the plane between which there are no three collinear and each point is assigned some color, so if...") (current)
- 15:36, 14 December 2023 (diff | hist) . . (+526) . . N 2013 OIM Problems/Problem 5 (Created page with "== Problem == Let <math>A</math> and <math>B</math> be two sets such that: 1. <math>A \cup B</math> is the set of positive integers. 2. <math>A \cap B</math> is empty. 3. I...") (current)
- 15:34, 14 December 2023 (diff | hist) . . (+881) . . N 2013 OIM Problems/Problem 4 (Created page with "== Problem == Let <math>\Gamma</math> be a circle with center <math>O</math>, <math>AE</math> be a diameter of <math>\Gamma</math> and <math>B</math> be the midpoint of one of...") (current)
- 15:32, 14 December 2023 (diff | hist) . . (+531) . . N 2013 OIM Problems/Problem 3 (Created page with "== Problem == Let <math>A = \left\{1, 2, 3, \cdots , n\right\}</math> with <math>n > 5</math>. Prove that there exists a finite set <math>B</math> of distinct positive integer...") (current)
- 15:29, 14 December 2023 (diff | hist) . . (+845) . . N 2013 OIM Problems/Problem 2 (Created page with "== Problem == Let <math>X</math>, <math>Y</math> be the ends of a diameter of a circle <math>\Gamma</math> and <math>N</math> the the midpoint of one of the <math>XY</math> ar...")
- 15:27, 14 December 2023 (diff | hist) . . (+855) . . N 2013 OIM Problems/Problem 1 (Created page with "== Problem == A set <math>S</math> of positive integers is called "''canalero''" if for any three numbers <math>a, b, c \in S</math>, all different, it holds that <math>a</mat...") (current)
- 15:23, 14 December 2023 (diff | hist) . . (+3) . . 2014 OIM Problems/Problem 6 (current)
- 15:23, 14 December 2023 (diff | hist) . . (-21) . . 2014 OIM Problems/Problem 6
- 15:22, 14 December 2023 (diff | hist) . . (+140) . . 2014 OIM Problems/Problem 6
- 15:21, 14 December 2023 (diff | hist) . . (+259) . . 2014 OIM Problems/Problem 6
- 15:19, 14 December 2023 (diff | hist) . . (+40) . . 2014 OIM Problems/Problem 6
- 15:18, 14 December 2023 (diff | hist) . . (+12) . . 2014 OIM Problems/Problem 6
- 15:17, 14 December 2023 (diff | hist) . . (+784) . . N 2014 OIM Problems/Problem 6 (Created page with "== Problem == Given a set <math>X</math> and a function <math>f: X \to X</math>, we say that for each <math>x \in X</math>, <math>f^1(x)=f(x)</math>, and for each <math>j \ge...")
- 15:13, 14 December 2023 (diff | hist) . . (+750) . . N 2014 OIM Problems/Problem 5 (Created page with "== Problem == Let <math>ABC</math> be an acute triangle and <math>H</math> be the point of intersection of the heights. The height from <math>A</math> cuts <math>BC</math> in...") (current)
- 15:11, 14 December 2023 (diff | hist) . . (+735) . . N 2014 OIM Problems/Problem 4 (Created page with "== Problem == There are <math>N</math> coins, of which <math>N-1</math> are authentic of equal weight and one is false, of different weight than the others. The objective is,...") (current)
- 15:09, 14 December 2023 (diff | hist) . . (+516) . . N 2014 OIM Problems/Problem 3 (Created page with "== Problem == 2014 points are marked on a circle. On each of the segments whose ends are two of the 2014 points, a non-negative real number is written. It's known that For any...") (current)
- 15:08, 14 December 2023 (diff | hist) . . (+348) . . N 2014 OIM Problems/Problem 2 (Created page with "== Problem == Find all the polynomials <math>P(x)</math> with real coefficients such that <math>P(2014) = 1</math> and, for some integer <math>c</math>, it holds that <cmath>...") (current)
- 15:07, 14 December 2023 (diff | hist) . . (+392) . . N 2014 OIM Problems/Problem 1 (Created page with "== Problem == For each positive integer <math>n</math>, define <math>s(n)</math> as the sum of the digits of <math>n</math>. Find the smallest positive integer <math>k</math>...") (current)
- 15:06, 14 December 2023 (diff | hist) . . (+1) . . 2015 OIM Problems/Problem 6 (current)
- 15:06, 14 December 2023 (diff | hist) . . (+31) . . 2015 OIM Problems/Problem 6 (→See also)
- 15:06, 14 December 2023 (diff | hist) . . (+31) . . 2015 OIM Problems/Problem 5 (→See also) (current)
- 15:05, 14 December 2023 (diff | hist) . . (+31) . . 2015 OIM Problems/Problem 4 (→See also) (current)
- 15:05, 14 December 2023 (diff | hist) . . (+31) . . 2015 OIM Problems/Problem 3 (→See also) (current)
- 15:05, 14 December 2023 (diff | hist) . . (+31) . . 2015 OIM Problems/Problem 2 (→See also) (current)
- 15:05, 14 December 2023 (diff | hist) . . (+31) . . 2015 OIM Problems/Problem 1 (current)
- 15:04, 14 December 2023 (diff | hist) . . (+488) . . N 2016 OIM Problems/Problem 6 (Created page with "== Problem == Let <math>k</math> be a positive integer and <math>a_1, a_2, \cdots a_k</math> be digits. Prove that a positive integer <math>n</math> exists such that the last...") (current)
- 15:01, 14 December 2023 (diff | hist) . . (-2) . . 2016 OIM Problems/Problem 5 (current)
- 15:01, 14 December 2023 (diff | hist) . . (+11) . . 2016 OIM Problems/Problem 5
- 15:01, 14 December 2023 (diff | hist) . . (+861) . . N 2016 OIM Problems/Problem 5 (Created page with "== Problem == The circles <math>\Gamma_1</math> and <math>\Gamma_2</math> intersect at two different points <math>A</math> and <math>K</math>. The tangent common to <math>\Gam...")
- 14:58, 14 December 2023 (diff | hist) . . (+540) . . N 2016 OIM Problems/Problem 4 (Created page with "== Problem == Find the greatest number of bishops that can be placed on an <math>8 \times 8</math> chess board, so that no two bishops are on the same square and each bishop i...") (current)
- 14:57, 14 December 2023 (diff | hist) . . (+1,052) . . N 2016 OIM Problems/Problem 3 (Created page with "== Problem == Let <math>ABC</math> be an acute triangle whose circumcircle is <math>\Gamma</math>. The tangents to <math>\Gamma</math> through <math>B</math> and <math>C</math...") (current)
- 14:53, 14 December 2023 (diff | hist) . . (+2) . . 2016 OIM Problems/Problem 2 (current)
- 14:53, 14 December 2023 (diff | hist) . . (+292) . . N 2016 OIM Problems/Problem 2 (Created page with "== Problem == Find all positive real solutions of the system of equations: <cmath>x=\frac{1}{y^2+y-1},\\y=\frac{1}{z^2+z-1},\\z=\frac{1}{x^2+x-1}</cmath> ~translated into Eng...")
- 14:51, 14 December 2023 (diff | hist) . . (+257) . . N 2016 OIM Problems/Problem 1 (Created page with "== Problem == Find all positive prime numbers <math>p, q, r, k</math> such that <cmath>pq + qr + rp = 12k + 1</cmath> ~translated into English by Tomas Diaz. ~orders@tomasdi...") (current)
- 14:50, 14 December 2023 (diff | hist) . . (+1) . . 2017 OIM Problems/Problem 6 (current)
- 14:50, 14 December 2023 (diff | hist) . . (+695) . . N 2017 OIM Problems/Problem 6 (Created page with "== Problem == Let <math>n > 2</math> be an even positive integer and <math>a_1 < a_2 < \cdots < a_n</math> real numbers such that <math>a_{k+1} -a_k \le 1</math> for all <math...")
- 14:46, 14 December 2023 (diff | hist) . . (+746) . . N 2017 OIM Problems/Problem 5 (Created page with "== Problem == Given a positive integer <math>n</math>, all its positive integer divisors are written in a blackboard. Ana and Beto play the following game: By turns, each one...") (current)
- 14:44, 14 December 2023 (diff | hist) . . (+868) . . N 2017 OIM Problems/Problem 4 (Created page with "== Problem == Let <math>ABC</math> be an acute triangle with <math>AC > AB</math> and <math>O</math> its circumcenter. Let <math>D</math> be a point on the segment <math>BC</m...") (current)
- 14:42, 14 December 2023 (diff | hist) . . (+536) . . N 2017 OIM Problems/Problem 3 (Created page with "== Problem == We consider configurations of integers: <math>a_{1,1},\\ a_{2,1}, a_{2,2},\\ a_{3,1}, a_{3,2}, a_{3,3},\\ \cdots\\ a_{2017,1}, a_{2017,2}, a_{2017,3},\cdots,a_{...") (current)
- 14:38, 14 December 2023 (diff | hist) . . (+11) . . 2017 OIM Problems/Problem 2 (current)
- 14:38, 14 December 2023 (diff | hist) . . (+814) . . N 2017 OIM Problems/Problem 2 (Created page with "== Problem == Let <math>ABC</math> be a right triangle and <math>\Gamma</math> its circumcircle. Let <math>D</math> be a point on the segment <math>BC</math>, distinct from <m...")
- 14:36, 14 December 2023 (diff | hist) . . (+11) . . 2017 OIM Problems/Problem 1 (current)
- 14:36, 14 December 2023 (diff | hist) . . (+686) . . N 2017 OIM Problems/Problem 1 (Created page with "== Problem == For each positive integer <math>n</math>, let <math>S(n)</math> be the sum of its digits. We say that <math>n</math> has the property <math>E</math> if the terms...")
- 14:33, 14 December 2023 (diff | hist) . . (+765) . . N 2018 OIM Problems/Problem 6 (Created page with "== Problem == Let <math>ABC</math> be an acute triangle with <math>AC > AB > BC</math>. The perpendicular bisectors of <math>AC</math> and <math>AB</math> cut the line <math>B...") (current)
- 14:30, 14 December 2023 (diff | hist) . . (+656) . . N 2018 OIM Problems/Problem 5 (Created page with "== Problem == Let <math>n</math> be a positive integer. For a permutation <math>a_1, a_2, \cdots , a_n,</math> of the numbers <math>1, 2, \cdots , n,</math> we define <cmath>...") (current)
- 14:26, 14 December 2023 (diff | hist) . . (+557) . . N 2018 OIM Problems/Problem 4 (Created page with "== Problem == A set "X" of positive integers is "''Iberian''" if <math>X</math> is a subset of <math>{2,3,4,\cdots,2018}</math>, and when <math>m</math> and <math>n</math> are...") (current)
- 14:22, 14 December 2023 (diff | hist) . . (+1,003) . . N 2018 OIM Problems/Problem 3 (Created page with "== Problem == In a plane we have <math>n</math> lines without two being parallel, nor two perpendicular, nor three concurrent. A system of Cartesian axes is chosen with one o...") (current)
- 14:19, 14 December 2023 (diff | hist) . . (+633) . . N 2018 OIM Problems/Problem 2 (Created page with "== Problem == Let <math>ABC</math> be a triangle such that <math>\angle BAC = 90^{\circ}</math> and <math>BA = CA</math>. Let <math>M</math> be the midpoint of <math>BC</math>...") (current)
- 14:17, 14 December 2023 (diff | hist) . . (+473) . . N 2018 OIM Problems/Problem 1 (Created page with "== Problem == For each natural number <math>n \ge 2</math>, find the integer solutions to the following system of equations: <cmath>x_1 = (x_2 + x_3 + x_4 + \cdots + x_n)^{20...") (current)
- 14:15, 14 December 2023 (diff | hist) . . (+4) . . 2019 OIM Problems/Problem 6 (current)
- 14:14, 14 December 2023 (diff | hist) . . (+439) . . N 2019 OIM Problems/Problem 6 (Created page with "== Problem == Let <math>a_1, a_2, \cdots , a_{2019}</math> be positive integers and <math>P</math> be a polynomial with integer coefficients such that, for every positive inte...")
- 14:12, 14 December 2023 (diff | hist) . . (+813) . . N 2019 OIM Problems/Problem 5 (Created page with "== Problem == Don Miguel places a game piece on one of the <math>(n + 1)^2</math> vertices defined by a <math>n \times n</math> board. A ''move'' consists of moving the piece...") (current)
- 14:07, 14 December 2023 (diff | hist) . . (+759) . . N 2019 OIM Problems/Problem 4 (Created page with "== Problem == Let <math>ABCD</math> be a trapezoid with <math>AB \parallel CD</math> and inscribed in the circle <math>\Gamma</math>. Let <math>P</math> and <math>Q</math> be...") (current)
- 14:05, 14 December 2023 (diff | hist) . . (+1,217) . . N 2019 OIM Problems/Problem 3 (Created page with "== Problem == Let <math>\Gamma</math> be the circumcircle of triangle <math>ABC</math>. The parallel to <math>AC</math> that passes through <math>B</math> cuts <math>\Gamma</m...") (current)
- 14:02, 14 December 2023 (diff | hist) . . (+378) . . N 2019 OIM Problems/Problem 2 (Created page with "== Problem == Find all polynomials <math>P(x)</math> of degree <math>n \ge 1</math> with integer coefficients such that for every real number <math>x</math> it holds <cmath>P...") (current)
- 14:00, 14 December 2023 (diff | hist) . . (+397) . . N 2019 OIM Problems/Problem 1 (Created page with "== Problem == For each positive integer <math>n</math>, let <math>s(n)</math> be the sum of the squares of the digits of <math>n</math>. For example, <math>s(15) = 1^2 + 5^2 =...") (current)
- 13:59, 14 December 2023 (diff | hist) . . (+819) . . N 2020 OIM Problems/Problem 6 (Created page with "== Problem == Let <math>ABC</math> be an acute and scalene triangle. Let <math>H</math> be the orthocenter and <math>O</math> the circumcenter of triangle <math>ABC</math>, an...") (current)
- 13:57, 14 December 2023 (diff | hist) . . (+309) . . N 2020 OIM Problems/Problem 5 (Created page with "== Problem == Find all functions <math>f : \mathbb{R} \to \mathbb{R}</math> such that <cmath>f(xf(x-y))+yf(x)=x+y+f(x^2)</cmath> for any real numbers <math>x, y</math>. ~tr...") (current)
- 13:55, 14 December 2023 (diff | hist) . . (+572) . . N 2020 OIM Problems/Problem 4 (Created page with "== Problem == Prove that there exists a set <math>C</math> of 2020 positive and distinct integers that simultaneously fulfills the following properties: * When we calculate...") (current)
- 13:53, 14 December 2023 (diff | hist) . . (+15) . . 2020 OIM Problems/Problem 3
- 13:52, 14 December 2023 (diff | hist) . . (+1) . . 2020 OIM Problems/Problem 3
- 13:52, 14 December 2023 (diff | hist) . . (+987) . . N 2020 OIM Problems/Problem 3 (Created page with "== Problem == Let <math>n \ge 2</math> be an integer. A sequence <math>\alpha = (a_1, a_2, \cdots , a_n)</math> of <math>n</math> integers is "''Limeña''" (from Lima, Perú)...")
- 13:45, 14 December 2023 (diff | hist) . . (+608) . . N 2020 OIM Problems/Problem 2 (Created page with "== Problem == For each positive integer <math>n</math>, define <math>T_n</math> as the smallest positive integer such that <math>1 + 2 + \cdots + T_n</math> is a multiple of <...") (current)
- 13:43, 14 December 2023 (diff | hist) . . (+305) . . 2020 OIM Problems/Problem 1 (current)
- 13:40, 14 December 2023 (diff | hist) . . (+542) . . N 2020 OIM Problems/Problem 1 (Created page with "== Problem == Let ABC be an acute triangle such that AB < AC. The midpoints of the Sides AB and AC are M and N, respectively. Let P and Q be points on the line MN such that \C...")
- 13:35, 14 December 2023 (diff | hist) . . (+851) . . N 2015 OIM Problems/Problem 6 (Created page with "== Problem == Beto plays the following game with his computer: initially his computer randomly chooses 30 numbers from 1 to 2015, and Beto writes them on a blackboard (there m...")
- 13:33, 14 December 2023 (diff | hist) . . (+217) . . N 2015 OIM Problems/Problem 5 (Created page with "== Problem == Find all pairs <math>(a, b)</math> of integers that verify: <cmath>(b^2+7(a-b))^2=a^3b</cmath> ~translated into English by Tomas Diaz. ~orders@tomasdiaz.com =...")
- 13:32, 14 December 2023 (diff | hist) . . (+663) . . N 2015 OIM Problems/Problem 4 (Created page with "== Problem == In acute triangle <math>ABC</math>, point <math>D</math> is the foot of the perpendicular from <math>A</math> on side <math>BC</math>. Let <math>P</math> be a po...")
- 13:30, 14 December 2023 (diff | hist) . . (+554) . . N 2015 OIM Problems/Problem 3 (Created page with "== Problem == Let <math>\alpha</math> and <math>\beta</math> be roots of the polynomial <math>x^2-qx+1</math>, where <math>q</math> is a rational number greater than 2. We de...")
- 13:24, 14 December 2023 (diff | hist) . . (+523) . . N 2015 OIM Problems/Problem 2 (Created page with "== Problem == A line <math>r</math> contains the points <math>A</math>, <math>B</math>, <math>C</math> and <math>D</math> in that order. Let <math>P</math> be a point outside...")
- 13:22, 14 December 2023 (diff | hist) . . (+308) . . N 2015 OIM Problems/Problem 1 (Created page with "== Problem == The number 125 can be represented as the sum of several natural numbers that are greater than 1 and coprime two to two. Find the maximum number of sums that can...")
- 04:50, 14 December 2023 (diff | hist) . . (0) . . 2002 OIM Problems/Problem 6 (current)
- 04:49, 14 December 2023 (diff | hist) . . (0) . . 2002 OIM Problems/Problem 6
- 04:49, 14 December 2023 (diff | hist) . . (+524) . . 2002 OIM Problems/Problem 6
- 04:45, 14 December 2023 (diff | hist) . . (+2) . . 2002 OIM Problems/Problem 5 (current)
- 04:45, 14 December 2023 (diff | hist) . . (-242) . . 2002 OIM Problems/Problem 5
- 04:43, 14 December 2023 (diff | hist) . . (-1) . . 2002 OIM Problems/Problem 4 (→Problem) (current)
- 04:43, 14 December 2023 (diff | hist) . . (+40) . . 2002 OIM Problems/Problem 4
- 04:41, 14 December 2023 (diff | hist) . . (+12) . . 2002 OIM Problems/Problem 3 (current)
- 04:41, 14 December 2023 (diff | hist) . . (-644) . . 2002 OIM Problems/Problem 3
- 04:39, 14 December 2023 (diff | hist) . . (-290) . . 2002 OIM Problems/Problem 2 (current)
- 04:38, 14 December 2023 (diff | hist) . . (-3) . . 2002 OIM Problems/Problem 1 (current)
- 04:37, 14 December 2023 (diff | hist) . . (-125) . . 2002 OIM Problems/Problem 1
- 04:35, 14 December 2023 (diff | hist) . . (-5) . . 2003 OIM Problems/Problem 6 (current)
- 04:34, 14 December 2023 (diff | hist) . . (-1) . . 2003 OIM Problems/Problem 6
- 04:34, 14 December 2023 (diff | hist) . . (+1) . . 2003 OIM Problems/Problem 6
- 04:33, 14 December 2023 (diff | hist) . . (+469) . . N 2003 OIM Problems/Problem 6 (Created page with "== Problem == Sequences <math>(a_n</math>)_{n \ge 0}, and <math>(b_n)_{n \ge 0}</math> with are defined by: <cmath>a_0=1 \text{, }b_0=4\text{, and}</cmath> <cmath>a_{n+1}=a_...")
- 04:32, 14 December 2023 (diff | hist) . . (+644) . . N 2003 OIM Problems/Problem 5 (Created page with "== Problem == In the square <math>ABCD</math>, let <math>P</math> and <math>Q</math> be points belonging to the sides <math>BC</math> and <math>CD</math> respectively, differe...") (current)
- 04:32, 14 December 2023 (diff | hist) . . (+547) . . N 2003 OIM Problems/Problem 4 (Created page with "== Problem == Let <math>M = {1, 2, \cdots , 49}</math> be the set of the first <math>49</math> positive integers. Determine the maximum integer <math>k</math> such that the se...") (current)
- 04:31, 14 December 2023 (diff | hist) . . (+1,102) . . N 2003 OIM Problems/Problem 3 (Created page with "== Problem == Pablo was copying the following problem from a blackboard: <cmath>\textit{Consider all sequences of 2004 real numbers }(x_0,x_1,x_2,\cdots , x_{2003})\textit{,...") (current)
- 04:30, 14 December 2023 (diff | hist) . . (+672) . . N 2003 OIM Problems/Problem 2 (Created page with "== Problem == Let <math>C</math> and <math>D</math> be two points on the semicircle of diameter <math>AB</math> such that <math>B</math> and <math>C</math> are in different se...") (current)
- 04:29, 14 December 2023 (diff | hist) . . (+684) . . N 2003 OIM Problems/Problem 1 (Created page with "== Problem == a) There are two sequences, each of 2003 consecutive integers, and a board with 2 rows and 2003 columns Decide if it is always possible to distribute the numbe...") (current)
- 04:27, 14 December 2023 (diff | hist) . . (+249) . . N 2001 OIM Problems/Problem 6 (Created page with "== Problem == Prove that it is impossible to cover a square of side 1 with five equal squares with sides less than <math>\frac{1}{2}</math> ~translated into English by Toma...") (current)
- 04:26, 14 December 2023 (diff | hist) . . (0) . . 2001 OIM Problems/Problem 5 (current)
- 04:25, 14 December 2023 (diff | hist) . . (0) . . 2001 OIM Problems/Problem 5
- 04:25, 14 December 2023 (diff | hist) . . (+1) . . 2001 OIM Problems/Problem 5
- 04:24, 14 December 2023 (diff | hist) . . (-4) . . 2001 OIM Problems/Problem 5
- 04:24, 14 December 2023 (diff | hist) . . (+12) . . 2001 OIM Problems/Problem 5
- 04:23, 14 December 2023 (diff | hist) . . (+1,437) . . N 2001 OIM Problems/Problem 5 (Created page with "== Problem == On a <math>2000 \times 2001</math> board the squares have coordinates <math>(x, y)</math> with <math>x, y</math> integers, <math>0 \le x le 1999</math> and <mat...")
- 04:16, 14 December 2023 (diff | hist) . . (+498) . . N 2001 OIM Problems/Problem 4 (Created page with "== Problem == Find the maximum number of increasing arithmetic progressions of three terms that can have a sequence <math>a_1 < a_2 < \cdots < a_n</math> of <math>n \ge 3</ma...") (current)
- 04:12, 14 December 2023 (diff | hist) . . (+12) . . 2001 OIM Problems/Problem 3 (current)
- 04:12, 14 December 2023 (diff | hist) . . (+550) . . N 2001 OIM Problems/Problem 3 (Created page with "== Problem == Let <math>S</math> be a set of <math>n</math> elements and <math>S_1, S_2, \cdots , S_k</math> subsets of <math>S</math> (<math>k \ge 2</math>), such that each...")
- 04:09, 14 December 2023 (diff | hist) . . (+635) . . N 2001 OIM Problems/Problem 2 (Created page with "== Problem == The circle inscribed in the triangle <math>ABC</math> has center <math>O</math> and is tangent to the sides <math>BC</math>, <math>AC</math> and <math>AB</math>...") (current)
- 04:08, 14 December 2023 (diff | hist) . . (0) . . 2001 OIM Problems/Problem 1 (current)
- 04:07, 14 December 2023 (diff | hist) . . (+513) . . N 2001 OIM Problems/Problem 1 (Created page with "== Problem == We say that a natural number <math>n</math> is "''çharrúa''" if it simultaneously satisfies the following conditions: * All digits of <math>n</math> are grea...")
- 04:02, 14 December 2023 (diff | hist) . . (-2) . . 2021 OIM Problems/Problem 6 (current)
- 04:02, 14 December 2023 (diff | hist) . . (+398) . . N 2021 OIM Problems/Problem 6 (Created page with "== Problem == Consider a regular polygon with <math>n</math> sides, <math>n \ge 4</math>, and let <math>V</math> be a subset of <math>r</math> vertices of the polygon. Show t...")
- 04:01, 14 December 2023 (diff | hist) . . (+448) . . N 2021 OIM Problems/Problem 5 (Created page with "== Problem == For a finite set <math>C</math> of integers, we define <math>S(C)</math> to be the sum of the elements of <math>C</math>. Find two nonempty sets <math>A</math>...") (current)
- 04:00, 14 December 2023 (diff | hist) . . (+303) . . N 2021 OIM Problems/Problem 4 (Created page with "== Problem == Let <math>a,b,c,x,y,z</math> be real numbers such that <cmath>a^2+x^2=b^2+y^2=c^2+z^2=(a+b)^2+(x+y)^2=(b+c)^2+(y+z)^2=(c+a)^2+(z+x)^2</cmath> Show that <math>...") (current)
- 03:57, 14 December 2023 (diff | hist) . . (+2) . . 2021 OIM Problems/Problem 3 (current)
- 03:57, 14 December 2023 (diff | hist) . . (+572) . . N 2021 OIM Problems/Problem 3 (Created page with "== Problem == Let <math>a_1, a_2, a_3, \cdots</math> be a sequence of positive integers and let <math>b_1, b_2, b_3, \cdots</math> be the sequence of real numbers given by <...")
- 03:53, 14 December 2023 (diff | hist) . . (+11) . . 2021 OIM Problems/Problem 2 (current)
- 03:53, 14 December 2023 (diff | hist) . . (+1,011) . . N 2021 OIM Problems/Problem 2 (Created page with "== Problem == Consider an acute triangle <math>ABC</math>, with <math>AC > AB</math>, and let <math>\Gamma</math> be its circumcircle. Let <math>E</math> and <math>F</math>...")
- 03:50, 14 December 2023 (diff | hist) . . (+2) . . 2021 OIM Problems/Problem 1 (current)
- 03:50, 14 December 2023 (diff | hist) . . (+1,032) . . N 2021 OIM Problems/Problem 1 (Created page with "== Problem == Let <math>P = {p_1, p_2, \cdots p_{10}}</math> be a set of 10 different prime numbers and let <math>A</math> be the set of all integers greater than 1 such tha...")
- 03:45, 14 December 2023 (diff | hist) . . (+361) . . N 2022 OIM Problems/Problem 6 (Created page with "== Problem == Let <math>\mathbb{Z}^+</math> be the set of positive integers. Find all functions <math>f: \mathbb{Z}^+ \to \mathbb{Z}^+</math> for which <cmath>f(a)f(a + b)...") (current)
- 03:42, 14 December 2023 (diff | hist) . . (+714) . . N 2022 OIM Problems/Problem 5 (Created page with "== Problem == Let <math>ABC</math> be an acute triangle with circumcircle <math>\Gamma</math>. Let <math>P</math> and <math>Q</math> be points on the half-plane defined by <m...") (current)
- 03:41, 14 December 2023 (diff | hist) . . (+1,094) . . N 2022 OIM Problems/Problem 4 (Created page with "== Problem == Let <math>n > 2</math> be a positive integer. There is a horizontal row of <math>n</math> cells such that each cell is colored red or blue. A block is a contigu...") (current)
- 03:38, 14 December 2023 (diff | hist) . . (-2) . . 2022 OIM Problems/Problem 3 (current)
- 03:38, 14 December 2023 (diff | hist) . . (+12) . . 2022 OIM Problems/Problem 3
- 03:37, 14 December 2023 (diff | hist) . . (+463) . . N 2022 OIM Problems/Problem 3 (Created page with "== Problem == Let <math>\mathbb{R}</math> be the set of real numbers. Find all functions <math>f : \mathbb{R} \to \mathbb{R} satisfying the following conditions simultaneousl...")
- 03:35, 14 December 2023 (diff | hist) . . (+787) . . N 2022 OIM Problems/Problem 2 (Created page with "== Problem == Let <math>S = {13, 133, 1333, \cdots }</math> be the set of positive integers of the form <math>1\overset{n\text{-digits}}{\overbrace{3\cdots 3}}</math>, with <...") (current)
- 03:29, 14 December 2023 (diff | hist) . . (+11) . . 2022 OIM Problems/Problem 1 (current)
- 03:29, 14 December 2023 (diff | hist) . . (+635) . . N 2022 OIM Problems/Problem 1 (Created page with "== Problem == Let <math>ABC</math> be an equilateral triangle with circumcenter <math>O</math> and circumcircle <math>\Gamma</math>. Let <math>D</math> be a point on the mino...")
- 03:24, 14 December 2023 (diff | hist) . . (+667) . . N 2023 OIM Problems/Problem 6 (Created page with "== Problem == Let <math>P</math> be a polynomial of degree greater than or equal to 4 with integer coefficients. An integer <math>x</math> is called <math>P</math>-''represent...") (current)
- 03:21, 14 December 2023 (diff | hist) . . (+19) . . 2023 OIM Problems/Problem 5 (current)
- 03:21, 14 December 2023 (diff | hist) . . (-23) . . 2023 OIM Problems/Problem 5
- 03:20, 14 December 2023 (diff | hist) . . (+652) . . N 2023 OIM Problems/Problem 5 (Created page with "== Problem == A sequence <math>P_1, \cdots , P_n</math> of points in the plane (not necessarily distinct) is "''carioca''" if there exists a permutation <math>a_1, \cdots , a_...")
- 03:17, 14 December 2023 (diff | hist) . . (+520) . . N 2023 OIM Problems/Problem 4 (Created page with "== Problem == Let <math>B</math> and <math>C</math> be two fixed points in the plane. For each point <math>A</math>, outside of the line <math>BC</math>, let <math>G</math> be...") (current)
- 03:15, 14 December 2023 (diff | hist) . . (+759) . . N 2023 OIM Problems/Problem 3 (Created page with "== Problem == Ana and Beto play with a two pan balance scale. They have 2023 dumbbells labeled with their weights, which are the numbers 1, 2, . . . , 2023, with none of them...") (current)
- 03:13, 14 December 2023 (diff | hist) . . (+345) . . N 2023 OIM Problems/Problem 2 (Created page with "== Problem == Let <math>\mathbb{Z}</math> be the set of integers. Find all functions <math>f: \mathbb{Z} \to \mathbb{Z}</math> such that: <cmath>2023f(f(x))+2022x^2=2022f(x)+...") (current)
- 03:11, 14 December 2023 (diff | hist) . . (+351) . . N 2023 OIM Problems/Problem 1 (Created page with "== Problem == Let <math>n</math> be a positive integer. The following 35 multiplications are performed: <cmath>1 \cdot n,2 \cdot n,\cdots ,35 \cdot n</cmath> Show that in at...") (current)
- 01:45, 14 December 2023 (diff | hist) . . (+982) . . 1991 OIM Problems/Problem 1
- 01:39, 14 December 2023 (diff | hist) . . (0) . . 1991 OIM Problems/Problem 1
- 01:39, 14 December 2023 (diff | hist) . . (+6) . . 1991 OIM Problems/Problem 1
- 01:38, 14 December 2023 (diff | hist) . . (+31) . . 1991 OIM Problems/Problem 1
- 01:38, 14 December 2023 (diff | hist) . . (0) . . N File:1991 OIM p1.png (current)
- 01:38, 14 December 2023 (diff | hist) . . (+231) . . 1991 OIM Problems/Problem 1
- 00:54, 14 December 2023 (diff | hist) . . (+666) . . 1992 OIM Problems/Problem 1
- 00:49, 14 December 2023 (diff | hist) . . (+35) . . 1991 OIM Problems/Problem 4
- 00:48, 14 December 2023 (diff | hist) . . (+270) . . 1992 OIM Problems/Problem 1
- 00:43, 14 December 2023 (diff | hist) . . (+127) . . 1992 OIM Problems/Problem 1
- 00:41, 14 December 2023 (diff | hist) . . (+12) . . 1992 OIM Problems/Problem 1
- 00:41, 14 December 2023 (diff | hist) . . (+52) . . 1992 OIM Problems/Problem 1
- 00:40, 14 December 2023 (diff | hist) . . (+40) . . 1992 OIM Problems/Problem 1
- 00:39, 14 December 2023 (diff | hist) . . (+11) . . 1992 OIM Problems/Problem 1
- 00:39, 14 December 2023 (diff | hist) . . (+1,286) . . 1992 OIM Problems/Problem 1
- 00:29, 14 December 2023 (diff | hist) . . (+291) . . 1992 OIM Problems/Problem 1
- 00:26, 14 December 2023 (diff | hist) . . (+201) . . 1992 OIM Problems/Problem 1
- 00:23, 14 December 2023 (diff | hist) . . (+173) . . 1992 OIM Problems/Problem 1
- 23:48, 13 December 2023 (diff | hist) . . (+5) . . 1992 OIM Problems/Problem 4
- 23:47, 13 December 2023 (diff | hist) . . (-108) . . 1992 OIM Problems/Problem 4
- 23:40, 13 December 2023 (diff | hist) . . (+248) . . 1991 OIM Problems/Problem 4
- 23:38, 13 December 2023 (diff | hist) . . (+163) . . 1991 OIM Problems/Problem 4
- 23:36, 13 December 2023 (diff | hist) . . (+71) . . 1991 OIM Problems/Problem 4
- 23:35, 13 December 2023 (diff | hist) . . (+1,444) . . 1991 OIM Problems/Problem 4
- 23:31, 13 December 2023 (diff | hist) . . (+10) . . 1991 OIM Problems/Problem 4
- 23:31, 13 December 2023 (diff | hist) . . (-1) . . 1991 OIM Problems/Problem 4
- 23:30, 13 December 2023 (diff | hist) . . (-179) . . 1991 OIM Problems/Problem 4
- 23:25, 13 December 2023 (diff | hist) . . (0) . . 1991 OIM Problems/Problem 4
- 23:25, 13 December 2023 (diff | hist) . . (+115) . . 1991 OIM Problems/Problem 4
- 23:23, 13 December 2023 (diff | hist) . . (-1,198) . . 1991 OIM Problems/Problem 4
- 23:22, 13 December 2023 (diff | hist) . . (+1) . . 1991 OIM Problems/Problem 4
- 23:21, 13 December 2023 (diff | hist) . . (-4) . . 1991 OIM Problems/Problem 4
- 23:20, 13 December 2023 (diff | hist) . . (+15) . . 1991 OIM Problems/Problem 4
- 23:20, 13 December 2023 (diff | hist) . . (+1,343) . . 1991 OIM Problems/Problem 4
- 23:02, 13 December 2023 (diff | hist) . . (+1,134) . . 1991 OIM Problems/Problem 4
- 22:50, 13 December 2023 (diff | hist) . . (+13) . . 1991 OIM Problems/Problem 3
- 22:50, 13 December 2023 (diff | hist) . . (+6) . . 1991 OIM Problems/Problem 3
- 22:49, 13 December 2023 (diff | hist) . . (+27) . . 1991 OIM Problems/Problem 3
- 22:48, 13 December 2023 (diff | hist) . . (+174) . . 1991 OIM Problems/Problem 3
- 18:20, 13 December 2023 (diff | hist) . . (+192) . . 1991 OIM Problems/Problem 3
- 18:17, 13 December 2023 (diff | hist) . . (+163) . . 1991 OIM Problems/Problem 3
- 18:14, 13 December 2023 (diff | hist) . . (+361) . . 1991 OIM Problems/Problem 3
- 18:12, 13 December 2023 (diff | hist) . . (+119) . . 1991 OIM Problems/Problem 3
- 18:11, 13 December 2023 (diff | hist) . . (+113) . . 1991 OIM Problems/Problem 3
- 18:09, 13 December 2023 (diff | hist) . . (+213) . . 1991 OIM Problems/Problem 3
- 18:06, 13 December 2023 (diff | hist) . . (+11) . . 1991 OIM Problems/Problem 3
- 18:06, 13 December 2023 (diff | hist) . . (+949) . . 1991 OIM Problems/Problem 3
- 17:57, 13 December 2023 (diff | hist) . . (+11) . . 1991 OIM Problems/Problem 3
- 16:42, 13 December 2023 (diff | hist) . . (+510) . . N 2002 OIM Problems/Problem 6 (Created page with "== Problem == Sequences <math>a_n</math>, and <math>b_n</math> with <math>n \ge 0</math> are defined by: <cmath>a_0=1 \text{, }b_0=4\text{, and}</cmath> <cmath>a_{n+1}=a_n^{...")
- 16:38, 13 December 2023 (diff | hist) . . (+688) . . N 2002 OIM Problems/Problem 5 (Created page with "== Problem == In the square <math>ABCD</math>, let <math>P</math> and <math>Q</math> be points belonging to the sides <math>BC</math> and <math>CD</math> respectively, differe...")
- 16:37, 13 December 2023 (diff | hist) . . (+591) . . N 2002 OIM Problems/Problem 4 (Created page with "== Problem == Let <math>M = {1, 2, \cdots , 49}</math> be the set of the first <math>49</math> positive integers. Determine the maximum integer <math>k</math> such that the se...")
- 16:34, 13 December 2023 (diff | hist) . . (+18) . . 2002 OIM Problems/Problem 3
- 16:34, 13 December 2023 (diff | hist) . . (+1) . . 2002 OIM Problems/Problem 3
- 16:34, 13 December 2023 (diff | hist) . . (+2) . . 2002 OIM Problems/Problem 3
- 16:33, 13 December 2023 (diff | hist) . . (+4) . . 2002 OIM Problems/Problem 3
- 16:32, 13 December 2023 (diff | hist) . . (+15) . . 2002 OIM Problems/Problem 3
- 16:31, 13 December 2023 (diff | hist) . . (+7) . . 2002 OIM Problems/Problem 3
- 16:31, 13 December 2023 (diff | hist) . . (-2) . . 2002 OIM Problems/Problem 3
- 16:31, 13 December 2023 (diff | hist) . . (+1,101) . . N 2002 OIM Problems/Problem 3 (Created page with "== Problem == Pablo was copying the following problem: <cmath>\text{Consider all sequences of 2004 real numbers}(x_0,x_1,x_2,\cdots , x_{2003})\text{, such that}</cmath>\ <c...")
- 16:23, 13 December 2023 (diff | hist) . . (+716) . . N 2002 OIM Problems/Problem 2 (Created page with "== Problem == Let <math>C</math> and <math>D</math> be two points on the semicircle of diameter <math>AB</math> such that <math>B</math> and <math>C</math> are in different se...")
- 16:21, 13 December 2023 (diff | hist) . . (+728) . . N 2002 OIM Problems/Problem 1 (Created page with "== Problem == a) There are two sequences, each of 2003 consecutive integers, and a board with 2 rows and 2003 columns Decide if it is always possible to distribute the numbe...")
- 16:18, 13 December 2023 (diff | hist) . . (+493) . . N 2000 OIM Problems/Problem 6 (Created page with "== Problem == A convex hexagon is called "''pretty''" if it has four diagonals of length 1, whose ends include all the vertices of the hexagon. 1. Given any number <math>k</m...") (current)
- 16:17, 13 December 2023 (diff | hist) . . (+599) . . N 2000 OIM Problems/Problem 5 (Created page with "== Problem == There is a pile of 2000 stones. Two players take turns removing stones, alternately, according to the following rules: 1. On each move you can remove 1, 2, 3, 4...") (current)
- 16:16, 13 December 2023 (diff | hist) . . (+417) . . N 2000 OIM Problems/Problem 4 (Created page with "== Problem == From an infinite arithmetic progression <math>1, a_l, a_2, \cdots </math> of real numbers, terms are eliminated, obtaining an infinite geometric progression <mat...") (current)
- 16:15, 13 December 2023 (diff | hist) . . (+287) . . N 2000 OIM Problems/Problem 3 (Created page with "== Problem == Find all solutions to the equation <cmath>(x + 1)^y - x^z = 1</cmath> for <math>x, y, z</math> integers greater than 1. ~translated into English by Tomas Diaz...") (current)
- 16:14, 13 December 2023 (diff | hist) . . (+884) . . N 2000 OIM Problems/Problem 2 (Created page with "== Problem == Let <math>S_1</math> and <math>S_2</math> be two circles, with centers <math>O_1</math> and <math>O_2</math> respectively, secants in <math>M</math> and <math>N<...") (current)
- 16:12, 13 December 2023 (diff | hist) . . (+26) . . 2000 OIM Problems/Problem 1 (current)
- 16:11, 13 December 2023 (diff | hist) . . (+693) . . N 2000 OIM Problems/Problem 1 (Created page with "== Problem == A regular polygon with <math>n</math> sides (<math>n \ge 3</math>) is constructed and its vertices are numbered from 1 to <math>n</math>. All diagonals of the po...")
- 16:10, 13 December 2023 (diff | hist) . . (+958) . . N 1999 OIM Problems/Problem 6 (Created page with "== Problem == Let <math>A</math> and <math>B</math> be points on the plane and <math>C</math> be a point on the bisector of <math>AB</math>. A sequence <math>C_1, C_2, \cdots...") (current)
- 16:07, 13 December 2023 (diff | hist) . . (+586) . . N 1999 OIM Problems/Problem 5 (Created page with "== Problem == An acute triangle <math>ABC</math> is inscribed in a circle with center <math>O</math>. The heights of the triangle are <math>AD</math>, <math>BE</math> and <ma...") (current)
- 16:06, 13 December 2023 (diff | hist) . . (+349) . . N 1999 OIM Problems/Problem 4 (Created page with "== Problem == Let <math>B</math> be an integer greater than 10 such that each of its digits belongs to the set {1, 3, 7, 9}. Show that <math>B</math> has a prime factor greate...") (current)
- 16:04, 13 December 2023 (diff | hist) . . (0) . . 1999 OIM Problems/Problem 3 (current)
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