User contributions
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- 11:57, 30 January 2021 (diff | hist) . . (+54) . . 1989 IMO Problems/Problem 4 (current)
- 11:56, 30 January 2021 (diff | hist) . . (+11) . . 1989 IMO Problems/Problem 3 (current)
- 11:55, 30 January 2021 (diff | hist) . . (+3,052) . . 1989 IMO Problems/Problem 3
- 11:50, 30 January 2021 (diff | hist) . . (+97) . . 1989 IMO Problems/Problem 2 (current)
- 11:47, 30 January 2021 (diff | hist) . . (+2,959) . . N 1989 IMO Problems (Created page with "Problems of the 1989 IMO. ==Day I== ===Problem 1=== Prove that in the set <math> \{1,2, \ldots, 1989\}</math> can be expressed as the disjoint union of subsets <math> A_i...") (current)
- 11:39, 30 January 2021 (diff | hist) . . (+11) . . 1988 IMO Problems
- 11:38, 30 January 2021 (diff | hist) . . (+51) . . 1988 IMO Problems/Problem 5 (current)
- 11:38, 30 January 2021 (diff | hist) . . (+3,071) . . 1988 IMO Problems/Problem 5
- 11:36, 30 January 2021 (diff | hist) . . (+79) . . 1988 IMO Problems/Problem 4 (current)
- 11:35, 30 January 2021 (diff | hist) . . (+6,188) . . 1988 IMO Problems/Problem 3 (current)
- 11:32, 30 January 2021 (diff | hist) . . (+46) . . 1988 IMO Problems/Problem 2 (current)
- 11:32, 30 January 2021 (diff | hist) . . (+110) . . 1988 IMO Problems/Problem 1 (current)
- 11:29, 30 January 2021 (diff | hist) . . (+3,113) . . 1988 IMO Problems
- 11:12, 30 January 2021 (diff | hist) . . (-451) . . 1987 IMO Problems
- 11:12, 30 January 2021 (diff | hist) . . (0) . . 1986 IMO Problems/Problem 6 (current)
- 11:09, 30 January 2021 (diff | hist) . . (+5,094) . . N 1986 IMO Problems/Problem 6 (Created page with "==Problem== Given a finite set of points in the plane, each with integer coordinates, is it always possible to color the points red or white so that for any straight line <mat...")
- 11:06, 30 January 2021 (diff | hist) . . (+3,891) . . 1986 IMO Problems/Problem 5 (current)
- 11:02, 30 January 2021 (diff | hist) . . (+1,608) . . N 1986 IMO Problems/Problem 4 (Created page with "==Problem== Let <math>A,B</math> be adjacent vertices of a regular <math>n</math>-gon (<math>n\ge5</math>) with center <math>O</math>. A triangle <math>XYZ</math>, which is co...") (current)
- 11:01, 30 January 2021 (diff | hist) . . (+1,323) . . N 1986 IMO Problems/Problem 3 (Created page with "==Problem== To each vertex of a regular pentagon an integer is assigned, so that the sum of all five numbers is positive. If three consecutive vertices are assigned the number...")
- 00:04, 30 January 2021 (diff | hist) . . (+54) . . 1986 IMO Problems/Problem 2 (current)
- 00:04, 30 January 2021 (diff | hist) . . (-768) . . 1986 IMO Problems/Problem 1
- 00:04, 30 January 2021 (diff | hist) . . (+478) . . 1986 IMO Problems (current)
- 00:02, 30 January 2021 (diff | hist) . . (+10) . . 1985 IMO Problems/Problem 6 (→Solution 3) (current)
- 00:01, 30 January 2021 (diff | hist) . . (+9,032) . . 1985 IMO Problems/Problem 6
- 23:56, 29 January 2021 (diff | hist) . . (+54) . . 1985 IMO Problems/Problem 5
- 23:56, 29 January 2021 (diff | hist) . . (+54) . . 1985 IMO Problems/Problem 4 (current)
- 23:54, 29 January 2021 (diff | hist) . . (+149) . . 1985 IMO Problems
- 23:53, 29 January 2021 (diff | hist) . . (+3,693) . . N 1984 IMO Problems/Problem 6 (Created page with "==Problem== Let <math>a,b,c,d</math> be odd integers such that <math>0<a<b<c<d</math> and <math>ad=bc</math>. Prove that if <math>a+d=2^k</math> and <math>b+c=2^m</math> for s...") (current)
- 23:50, 29 January 2021 (diff | hist) . . (+1,348) . . N 1984 IMO Problems/Problem 5 (Created page with "==Problem== Let <math> d</math> be the sum of the lengths of all the diagonals of a plane convex polygon with <math> n</math> vertices (where <math> n>3</math>). Let <math> p<...") (current)
- 23:49, 29 January 2021 (diff | hist) . . (+38) . . 1984 IMO Problems/Problem 4 (current)
- 23:49, 29 January 2021 (diff | hist) . . (0) . . 1984 IMO Problems/Problem 3 (current)
- 23:48, 29 January 2021 (diff | hist) . . (+2,105) . . N 1984 IMO Problems/Problem 3 (Created page with "==Problem== Given points <math>O</math> and <math>A</math> in the plane. Every point in the plane is colored with one of a finite number of colors. Given a point <math>X</math...")
- 23:47, 29 January 2021 (diff | hist) . . (+1,046) . . N 1984 IMO Problems/Problem 2 (Created page with "==Problem== Find one pair of positive integers <math>a,b</math> such that <math>ab(a+b)</math> is not divisible by <math>7</math>, but <math>(a+b)^7-a^7-b^7</math> is divisibl...") (current)
- 23:45, 29 January 2021 (diff | hist) . . (+68) . . 1984 IMO Problems/Problem 1
- 23:45, 29 January 2021 (diff | hist) . . (+2,467) . . N 1984 IMO Problems (Created page with "Problems of the 1984 IMO. ==Day I== ===Problem 1=== Prove that <math>0\le yz+zx+xy-2xyz\le{7\over27}</math>, where <math>x,y</math> and <math>z</math> are non-negative re...") (current)
- 23:41, 29 January 2021 (diff | hist) . . (+65) . . 1983 IMO Problems/Problem 6
- 23:40, 29 January 2021 (diff | hist) . . (+54) . . 1983 IMO Problems/Problem 5 (current)
- 23:40, 29 January 2021 (diff | hist) . . (0) . . 1983 IMO Problems/Problem 4 (current)
- 23:39, 29 January 2021 (diff | hist) . . (+1,678) . . 1983 IMO Problems/Problem 4
- 23:37, 29 January 2021 (diff | hist) . . (+3,372) . . 1983 IMO Problems/Problem 3 (current)
- 23:35, 29 January 2021 (diff | hist) . . (+6,572) . . 1983 IMO Problems/Problem 2 (current)
- 23:29, 29 January 2021 (diff | hist) . . (+878) . . N 1982 IMO Problems/Problem 6 (Created page with "==Problem== Let <math>S</math> be a square with sides length <math>100</math>. Let <math>L</math> be a path within <math>S</math> which does not meet itself and which is compo...")
- 23:27, 29 January 2021 (diff | hist) . . (0) . . 1982 IMO Problems/Problem 5
- 23:26, 29 January 2021 (diff | hist) . . (+3,095) . . N 1982 IMO Problems/Problem 5 (Created page with "==Problem== The diagonals <math>AC</math> and <math>CE</math> of the regular hexagon <math>ABCDEF</math> are divided by inner points <math>M</math> and <math>N</math> respecti...")
- 23:23, 29 January 2021 (diff | hist) . . (+2,646) . . N 1982 IMO Problems/Problem 3 (Created page with "==Problem== Consider infinite sequences <math>\{x_n\}</math> of positive reals such that <math>x_0=1</math> and <math>x_0\ge x_1\ge x_2\ge\ldots</math>. a) Prove that for eve...") (current)
- 23:19, 29 January 2021 (diff | hist) . . (+3,852) . . N 1982 IMO Problems/Problem 2 (Created page with "==Problem== A non-isosceles triangle <math>A_{1}A_{2}A_{3}</math> has sides <math>a_{1}</math>, <math>a_{2}</math>, <math>a_{3}</math> with the side <math>a_{i}</math> lying o...") (current)
- 23:17, 29 January 2021 (diff | hist) . . (0) . . 1982 IMO Problems/Problem 1 (current)
- 23:16, 29 January 2021 (diff | hist) . . (+4,340) . . N 1982 IMO Problems/Problem 1 (Created page with "==Problem== The function <math>f(n)</math> is defined on the positive integers and takes non-negative integer values. <math>f(2)=0,f(3)>0,f(9999)=3333</math> and for all <math...")
- 23:10, 29 January 2021 (diff | hist) . . (+1) . . 1982 IMO Problems (current)
- 23:09, 29 January 2021 (diff | hist) . . (+54) . . 1981 IMO Problems/Problem 5 (current)
- 23:06, 29 January 2021 (diff | hist) . . (+1,654) . . N 1979 IMO Problems/Problem 6 (Created page with "==Problem== Let <math>A</math> and <math>E</math> be opposite vertices of an octagon. A frog starts at vertex <math>A.</math> From any vertex except <math>E</math> it jumps to...") (current)
- 23:04, 29 January 2021 (diff | hist) . . (-239) . . 1979 IMO Problems/Problem 5
- 23:03, 29 January 2021 (diff | hist) . . (+668) . . N 1979 IMO Problems/Problem 5 (Created page with "==Problem== Determine all real numbers a for which there exists positive reals <math>x_{1}, \ldots, x_{5}</math> which satisfy the relations <math> \sum_{k=1}^{5} kx_{k}=a,</m...")
- 23:01, 29 January 2021 (diff | hist) . . (+155) . . 1979 IMO Problems/Problem 4 (current)
- 23:01, 29 January 2021 (diff | hist) . . (+3,734) . . N 1979 IMO Problems/Problem 4 (Created page with "==Problem== We consider a point <math>P</math> in a plane <math>p</math> and a point <math>Q \not\in p</math>. Determine all the points <math>R</math> from <math>p</math> for...")
- 22:55, 29 January 2021 (diff | hist) . . (+3) . . 1979 IMO Problems/Problem 3 (current)
- 22:55, 29 January 2021 (diff | hist) . . (-100) . . 1979 IMO Problems/Problem 3
- 22:54, 29 January 2021 (diff | hist) . . (+8,421) . . N 1979 IMO Problems/Problem 3 (Created page with "==Problem== Two circles in a plane intersect. <math>A</math> is one of the points of intersection. Starting simultaneously from <math>A</math> two points move with constant sp...")
- 22:50, 29 January 2021 (diff | hist) . . (+34) . . 1979 IMO Problems/Problem 2 (current)
- 22:49, 29 January 2021 (diff | hist) . . (+2,500) . . N 1979 IMO Problems/Problem 2 (Created page with "==Problem== We consider a prism which has the upper and inferior basis the pentagons: <math>A_{1}A_{2}A_{3}A_{4}A_{5}</math> and <math>B_{1}B_{2}B_{3}B_{4}B_{5}</math>. Each o...")
- 17:12, 29 January 2021 (diff | hist) . . (+45) . . 1979 IMO Problems/Problem 1 (current)
- 17:11, 29 January 2021 (diff | hist) . . (+1,773) . . N 1979 IMO Problems/Problem 1 (Created page with "==Problem== If <math>p</math> and <math>q</math> are natural numbers so that<cmath> \frac{p}{q}=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+ \ldots -\frac{1}{1318}+\frac{1}{1319}, <...")
- 17:10, 29 January 2021 (diff | hist) . . (+2,773) . . 1979 IMO Problems (current)
- 17:06, 29 January 2021 (diff | hist) . . (+66) . . 1978 IMO Problems/Problem 6
- 17:05, 29 January 2021 (diff | hist) . . (0) . . 1978 IMO Problems/Problem 5 (current)
- 17:05, 29 January 2021 (diff | hist) . . (+1,256) . . 1978 IMO Problems/Problem 5
- 17:04, 29 January 2021 (diff | hist) . . (+150) . . 1978 IMO Problems/Problem 4 (current)
- 17:03, 29 January 2021 (diff | hist) . . (+54) . . 1978 IMO Problems/Problem 4
- 17:03, 29 January 2021 (diff | hist) . . (+2,920) . . 1978 IMO Problems/Problem 4
- 17:01, 29 January 2021 (diff | hist) . . (+2,311) . . 1978 IMO Problems/Problem 3 (current)
- 17:00, 29 January 2021 (diff | hist) . . (+75) . . 1978 IMO Problems/Problem 2
- 16:59, 29 January 2021 (diff | hist) . . (+624) . . 1978 IMO Problems/Problem 2
- 16:57, 29 January 2021 (diff | hist) . . (+1,289) . . 1978 IMO Problems/Problem 1
- 16:56, 29 January 2021 (diff | hist) . . (+4) . . 1978 IMO Problems (current)
- 16:56, 29 January 2021 (diff | hist) . . (+2,726) . . 1978 IMO Problems
- 16:54, 29 January 2021 (diff | hist) . . (+33) . . 1977 IMO Problems (current)
- 16:51, 29 January 2021 (diff | hist) . . (+5) . . 1977 IMO Problems
- 16:49, 29 January 2021 (diff | hist) . . (0) . . 1977 IMO Problems/Problem 6 (current)
- 16:49, 29 January 2021 (diff | hist) . . (+66) . . 1977 IMO Problems/Problem 6
- 16:48, 29 January 2021 (diff | hist) . . (+2) . . 1977 IMO Problems/Problem 4 (current)
- 16:48, 29 January 2021 (diff | hist) . . (+8) . . 1977 IMO Problems/Problem 4
- 16:47, 29 January 2021 (diff | hist) . . (+1,646) . . 1977 IMO Problems/Problem 4
- 16:46, 29 January 2021 (diff | hist) . . (+1,298) . . N 1977 IMO Problems/Problem 5 (Created page with "==Problem== Let <math>a,b</math> be two natural numbers. When we divide <math>a^2+b^2</math> by <math>a+b</math>, we the the remainder <math>r</math> and the quotient <math>q....") (current)
- 16:46, 29 January 2021 (diff | hist) . . (-1,298) . . 1977 IMO Problems/Problem 4 (Blanked the page) (Tag: Blanking)
- 16:45, 29 January 2021 (diff | hist) . . (+38) . . 1977 IMO Problems/Problem 4
- 16:45, 29 January 2021 (diff | hist) . . (+1,260) . . N 1977 IMO Problems/Problem 4 (Created page with "==Problem== Let <math>a,b</math> be two natural numbers. When we divide <math>a^2+b^2</math> by <math>a+b</math>, we the the remainder <math>r</math> and the quotient <math>q....")
- 16:43, 29 January 2021 (diff | hist) . . (+1,993) . . N 1977 IMO Problems/Problem 3 (Created page with "==Problem== Let <math>n</math> be a given number greater than 2. We consider the set <math>V_n</math> of all the integers of the form <math>1 + kn</math> with <math>k = 1, 2,...") (current)
- 16:42, 29 January 2021 (diff | hist) . . (+1,201) . . N 1977 IMO Problems/Problem 2 (Created page with "==Problem== In a finite sequence of real numbers the sum of any seven successive terms is negative and the sum of any eleven successive terms is positive. Determine the maximu...") (current)
- 16:40, 29 January 2021 (diff | hist) . . (+1,172) . . N 1977 IMO Problems/Problem 1 (Created page with "==Problem== In the interior of a square <math>ABCD</math> we construct the equilateral triangles <math>ABK, BCL, CDM, DAN.</math> Prove that the midpoints of the four segments...") (current)
- 16:39, 29 January 2021 (diff | hist) . . (+2,714) . . N 1977 IMO Problems (Created page with "Problems of the 1977 IMO in Yugoslavia. ==Problem 1== In the interior of a square <math>ABCD</math> we construct the equilateral triangles <math>ABK, BCL, CDM, DAN.</math...")
- 16:30, 29 January 2021 (diff | hist) . . (-4) . . 1976 IMO Problems/Problem 6 (current)
- 16:29, 29 January 2021 (diff | hist) . . (-6) . . 1976 IMO Problems/Problem 6
- 16:29, 29 January 2021 (diff | hist) . . (-28) . . 1976 IMO Problems/Problem 6
- 16:28, 29 January 2021 (diff | hist) . . (+1,381) . . 1976 IMO Problems/Problem 5 (current)
- 16:27, 29 January 2021 (diff | hist) . . (-2) . . 1976 IMO Problems/Problem 3 (current)
- 16:26, 29 January 2021 (diff | hist) . . (+10) . . 1976 IMO Problems/Problem 3
- 16:25, 29 January 2021 (diff | hist) . . (+5) . . 1976 IMO Problems (current)
- 16:25, 29 January 2021 (diff | hist) . . (+12) . . 1976 IMO Problems
- 16:24, 29 January 2021 (diff | hist) . . (+234) . . 1976 IMO Problems
- 16:23, 29 January 2021 (diff | hist) . . (+1) . . 1976 IMO Problems
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