# User contributions

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- 00:26, 17 March 2020
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**(+3,048)** . . 1989 IMO Problems/Problem 1 (→Problem) (current) - 00:05, 17 March 2020 (diff | hist) . . (+15) . . 1989 IMO Problems/Problem 1
- 00:01, 17 March 2020 (diff | hist) . . (+283) . . N 1989 IMO Problems/Problem 1 (Created page with "Prove that in the set <math> \{1,2, \ldots, 1989\}</math> can be expressed as the disjoint union of subsets <math> A_i, \{i = 1,2, \ldots, 117\}</math> such that i.) each <ma...")
- 13:48, 15 March 2020 (diff | hist) . . (+18) . . 1988 IMO Problems/Problem 2 (→Solution) (current)
- 01:28, 15 March 2020 (diff | hist) . . (+10) . . 1988 IMO Problems/Problem 2 (→Solution)
- 01:24, 15 March 2020
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**(+2,702)** . . 1988 IMO Problems/Problem 2 - 19:40, 2 February 2019
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**(+2,122)** . . N 2018 JBMO Problems/Problem 4 (Created page with "== Problem == Let <math>\triangle ABC</math> and <math>A'</math>,<math>B'</math>,<math>C'</math> the symmetrics of vertex over opposite sides.The intersection of the circumci...") (current) - 18:51, 2 February 2019
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**(+559)** . . N 2018 JBMO (Created page with "'''2018 JBMO''' problems and solutions. The 22nd JBMO was held in Rhodes, Hellas on 19-24 June 2018. * 2018 JBMO Problems * Problem 1 *...") (current) - 18:49, 2 February 2019 (diff | hist) . . (+77) . . Junior Balkan Mathematical Olympiad (current)
- 21:49, 18 January 2019
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**(+1,195)** . . N 2013 JBMO Problems/Problem 1 (Created page with "==Problem== Find all ordered pairs <math>(a,b)</math> of positive integers for which the numbers <math>\dfrac{a^3b-1}{a+1}</math> and <math>\dfrac{b^3a+1}{b-1}</math> are bot...") (current) - 21:11, 18 January 2019
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**(+550)** . . N 2013 JBMO (Created page with "'''2013 JBMO''' problems and solutions. The 17th JBMO was held in Antalya, Turkey in June, 2013. * 2013 JBMO Problems * Problem 1 * 2...") (current) - 00:22, 3 January 2019
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**(+1,610)** . . N 2008 JBMO Problems/Problem 3 (Created page with "==Problem== Find all prime numbers <math> p,q,r</math>, such that <math> \frac{p}{q}-\frac{4}{r+1}=1</math> == Solution == The given equation can be rearranged into the be...") (current) - 00:06, 3 January 2019
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**(+550)** . . N 2008 JBMO (Created page with "'''2008 JBMO''' problems and solutions. The 12th JBMO was held in Vlorë, Albania in June, 2008. * 2008 JBMO Problems * Problem 1 * 2...") (current) - 11:16, 31 December 2018
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**(+2,700)** . . N 2006 JBMO Problems/Problem 4 (Created page with "==Problem== Consider a <math>2n \times 2n</math> board. From the <math>i</math>th line we remove the central <math>2(i-1)</math> unit squares. What is the maximal number of r...") (current) - 23:11, 26 December 2018 (diff | hist) . . (+1) . . 2006 JBMO Problems/Problem 1 (current)
- 23:10, 26 December 2018 (diff | hist) . . (-1) . . 2006 JBMO Problems/Problem 1
- 23:04, 26 December 2018 (diff | hist) . . (+42) . . 2006 JBMO Problems/Problem 1
- 23:02, 26 December 2018 (diff | hist) . . (-4) . . 2006 JBMO Problems/Problem 1
- 22:58, 26 December 2018
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**(+1,273)** . . N 2006 JBMO Problems/Problem 1 (Created page with "==Problem== If <math>n>4</math> is a composite number, then <math>2n</math> divides <math>(n-1)!</math>. == Solution == We shall prove a more stronger result that <math>4n...") - 22:44, 26 December 2018
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**(+558)** . . N 2006 JBMO (Created page with "'''2006 JBMO''' problems and solutions. The 10th JBMO was held in Chişinău, Moldova in 2006. * 2006 JBMO Problems ** Problem 1 ** 2...") (current) - 02:18, 25 December 2018 (diff | hist) . . (+269) . . 2005 JBMO Problems/Problem 1
- 01:55, 23 December 2018
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**(+1,082)** . . N 2005 JBMO Problems/Problem 1 (Created page with "==Problem 1== Find all positive integers <math>x,y</math> satisfying the equation <cmath> 9(x^2+y^2+1) + 2(3xy+2) = 2005 . </cmath> == Solution == We can re-write the equa...") - 01:03, 23 December 2018
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**(+2,525)** . . N 2004 JBMO Problems/Problem 4 (Created page with "==Problem== Consider a convex polygon having <math>n</math> vertices, <math>n\geq 4</math>. We arbitrarily decompose the polygon into triangles having all the vertices among...") (current) - 00:22, 18 December 2018 (diff | hist) . . (+2) . . 2004 JBMO Problems/Problem 2
- 00:21, 18 December 2018
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**(+1,695)** . . N 2004 JBMO Problems/Problem 2 (Created page with "==Problem== Let <math>ABC</math> be an isosceles triangle with <math>AC=BC</math>, let <math>M</math> be the midpoint of its side <math>AC</math>, and let <math>Z</math> be t...") - 00:15, 17 December 2018 (diff | hist) . . (-5) . . 2004 JBMO Problems/Problem 1 (→Solution) (current)
- 00:15, 17 December 2018 (diff | hist) . . (+1) . . 2004 JBMO Problems/Problem 1 (→Solution)
- 00:14, 17 December 2018 (diff | hist) . . (-5) . . 2004 JBMO Problems/Problem 1
- 00:07, 17 December 2018
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**(+796)** . . N 2004 JBMO Problems/Problem 1 (Created page with "==Problem== Prove that the inequality <cmath> \frac{ x+y}{x^2-xy+y^2 } \leq \frac{ 2\sqrt 2 }{\sqrt{ x^2 +y^2 } } </cmath> holds for all real numbers <math>x</math> and <math...") - 22:53, 13 December 2018 (diff | hist) . . (-1) . . 2003 JBMO Problems/Problem 3 (current)
- 22:49, 13 December 2018 (diff | hist) . . (-4) . . 2003 JBMO Problems/Problem 3
- 01:00, 13 December 2018 (diff | hist) . . (0) . . 2003 JBMO Problems/Problem 3 (→Solution)
- 23:30, 12 December 2018 (diff | hist) . . (-1) . . 2003 JBMO Problems/Problem 3 (→Solution)
- 16:36, 12 December 2018 (diff | hist) . . (+22) . . 2003 JBMO Problems/Problem 3
- 16:35, 12 December 2018
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**(+4,240)** . . N 2003 JBMO Problems/Problem 3 (Created page with "==Problem== Let <math>D</math>, <math>E</math>, <math>F</math> be the midpoints of the arcs <math>BC</math>, <math>CA</math>, <math>AB</math> on the circumcircle of a triangl...") - 16:38, 9 December 2018
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**(+2,573)** . . N 2002 JBMO Problems/Problem 2 (Created page with "==Problem== Two circles with centers <math>O_{1}</math> and <math>O_{2}</math> meet at two points <math>A</math> and <math>B</math> such that the centers of the circles are o...") (current) - 21:37, 8 December 2018
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**(+1,365)** . . N 2002 JBMO Problems/Problem 1 (Created page with "==Problem== The triangle <math>ABC</math> has <math>CA = CB</math>. <math>P</math> is a point on the circumcircle between <math>A</math> and <math>B</math> (and on the opposi...") (current) - 18:37, 8 December 2018
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**(+3,130)** . . N 2001 JBMO Problems/Problem 3 (Created page with "==Problem 3== Let <math>ABC</math> be an equilateral triangle and <math>D,E</math> on the sides <math>[AB]</math> and <math>[AC]</math> respectively. If <math>DF,EG</math> (...") (current) - 18:09, 8 December 2018 (diff | hist) . . (-255) . . 2001 JBMO Problems (→Problem 3) (current)
- 17:37, 8 December 2018 (diff | hist) . . (+358) . . 2001 JBMO Problems (→Problem 3)
- 00:53, 5 December 2018 (diff | hist) . . (+21) . . 1990 AIME Problems/Problem 11 (current)
- 00:41, 5 December 2018 (diff | hist) . . (0) . . N File:Problem 3 Pic.jpg (current)
- 00:35, 5 December 2018 (diff | hist) . . (+136) . . 2000 JBMO Problems/Problem 3 (current)
- 00:21, 5 December 2018 (diff | hist) . . (-1) . . 2000 JBMO Problems/Problem 3
- 00:09, 5 December 2018
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**(+2,060)** . . N 2000 JBMO Problems/Problem 3 (Created page with "==Problem 3== A half-circle of diameter <math>EF</math> is placed on the side <math>BC</math> of a triangle <math>ABC</math> and it is tangent to the sides <math>AB</math> an...") - 00:25, 4 December 2018 (diff | hist) . . (+125) . . 2000 JBMO Problems/Problem 2 (→Solution) (current)
- 00:24, 4 December 2018 (diff | hist) . . (0) . . 2000 JBMO Problems/Problem 1 (current)
- 00:20, 4 December 2018
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**(+580)** . . 1999 JBMO Problems/Problem 4 - 00:18, 4 December 2018 (diff | hist) . . (+216) . . 1998 JBMO Problems/Problem 2
- 00:12, 4 December 2018
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**(+826)** . . N 2000 JBMO Problems/Problem 2 (Created page with "== Solution == After rearranging we get: <math>(k-n)(k+n) = 3^n</math> Let <math>k-n = 3^a, k+n = 3^{n-a}</math> we get: <math>2n = 3^a(3^{n-2a} - 1)</math> or, <math>(2n/(...")

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