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- 21:57, 13 June 2012 (diff | hist) . . (+582) . . m 1983 AIME Problems/Problem 11
- 21:48, 13 June 2012 (diff | hist) . . (+3,776) . . m 2011 AMC 10A Problems/Problem 25
- 19:15, 7 May 2012 (diff | hist) . . (-439) . . 2006 Romanian NMO Problems/Grade 10/Problem 1
- 21:10, 19 April 2012 (diff | hist) . . (-17) . . 2012 AIME II Problems/Problem 13 (→Solution)
- 21:00, 19 April 2012 (diff | hist) . . (+176) . . Artinian (current)
- 19:01, 7 April 2012 (diff | hist) . . (+47) . . m Category (category theory) (→Examples) (current)
- 18:38, 7 April 2012 (diff | hist) . . (+687) . . m Category (category theory) (→Examples)
- 18:08, 7 April 2012 (diff | hist) . . (+76) . . m Prime ideal (current)
- 00:35, 31 March 2012 (diff | hist) . . (+154) . . m AoPS Wiki:FAQ (Reverted edits by Basketball12 (talk) to last revision by Bluecarneal)
- 18:44, 17 March 2012 (diff | hist) . . (+4) . . m 2012 AIME I Problems/Problem 12 (→Solution)
- 17:54, 16 March 2012 (diff | hist) . . (+35) . . m Free group (current)
- 17:52, 16 March 2012 (diff | hist) . . (+63) . . m Algebraic number (→Properties)
- 17:49, 16 March 2012 (diff | hist) . . (+282) . . m Field
- 17:46, 16 March 2012 (diff | hist) . . (+499) . . m Commutative property (→Examples) (current)
- 17:43, 16 March 2012 (diff | hist) . . (+41) . . m Integral domain (→Examples) (current)
- 17:25, 16 March 2012 (diff | hist) . . (+254) . . m Relatively prime
- 17:15, 16 March 2012 (diff | hist) . . (+1,389) . . 2012 AMC 10A Problems/Problem 25 (→Appendix)
- 22:10, 15 March 2012 (diff | hist) . . (+2,035) . . 2012 AMC 10A Problems/Problem 25
- 21:13, 15 March 2012 (diff | hist) . . (-20) . . m 2012 AMC 10A Problems/Problem 25
- 15:03, 23 January 2012 (diff | hist) . . (+556) . . 2006 AMC 10A Problems/Problem 24
- 13:42, 23 January 2012 (diff | hist) . . (-492) . . 2006 AMC 10B Problems/Problem 25 (→Solution)
- 13:43, 13 January 2012 (diff | hist) . . (+1,273) . . 2004 AMC 10A Problems/Problem 23
- 13:07, 13 January 2012 (diff | hist) . . (+781) . . 2004 AMC 12A Problems/Problem 18
- 12:50, 13 January 2012 (diff | hist) . . (+878) . . 2003 AMC 12A Problems/Problem 15
- 22:26, 25 December 2011 (diff | hist) . . (+154) . . m 2005 AMC 12A Problems/Problem 5
- 13:08, 17 August 2011 (diff | hist) . . (-3) . . m 2001 IMO Shortlist Problems/N6 (→First Solution) (current)
- 00:23, 15 August 2011 (diff | hist) . . (+5) . . m 2008 AMC 12B Problems/Problem 9 (→Solution 1)
- 00:21, 15 August 2011 (diff | hist) . . (+511) . . 2008 AMC 12B Problems/Problem 9
- 00:10, 15 August 2011 (diff | hist) . . (+12) . . m Trigonometric identities (→Further Conclusions)
- 18:44, 14 August 2011 (diff | hist) . . (+640) . . Ellipse
- 20:25, 3 August 2011 (diff | hist) . . (+1,714) . . Chicken McNugget Theorem
- 17:57, 3 August 2011 (diff | hist) . . (+34) . . m Chicken McNugget Theorem
- 21:23, 23 July 2011 (diff | hist) . . (-143) . . m 2009 AMC 8 Problems
- 17:06, 23 July 2011 (diff | hist) . . (-105) . . m 2011 IMO Problems
- 23:27, 7 July 2011 (diff | hist) . . (+581) . . m 2006 Romanian NMO Problems/Grade 7/Problem 4 (current)
- 22:39, 7 July 2011 (diff | hist) . . (+1,827) . . m 2006 Romanian NMO Problems/Grade 7/Problem 4
- 16:04, 26 June 2011 (diff | hist) . . (-302) . . m Autograph (→The code)
- 21:21, 25 June 2011 (diff | hist) . . (-436) . . Autograph (→The code: edited for readability)
- 19:37, 25 June 2011 (diff | hist) . . (+317) . . AoPS Wiki:FAQ
- 19:14, 25 June 2011 (diff | hist) . . (+159) . . AoPS Wiki:FAQ
- 19:06, 25 June 2011 (diff | hist) . . (+42) . . AoPS Wiki:FAQ (→Where can I find examples of Asymptote diagrams and code?)
- 00:06, 10 June 2011 (diff | hist) . . (-55) . . m 1998 AJHSME Problems/Problem 1 (→See also)
- 00:05, 10 June 2011 (diff | hist) . . (-69) . . m 1998 AJHSME Problems/Problem 2 (→See also)
- 00:05, 10 June 2011 (diff | hist) . . (-69) . . m 1998 AJHSME Problems/Problem 3 (→See also)
- 00:04, 10 June 2011 (diff | hist) . . (-69) . . m 1998 AJHSME Problems/Problem 4 (→See also)
- 00:03, 10 June 2011 (diff | hist) . . (-69) . . m 1998 AJHSME Problems/Problem 5 (→See also)
- 00:03, 10 June 2011 (diff | hist) . . (-69) . . m 1998 AJHSME Problems/Problem 6 (→See also)
- 00:00, 10 June 2011 (diff | hist) . . (-69) . . m 1998 AJHSME Problems/Problem 7 (→See also)
- 00:00, 10 June 2011 (diff | hist) . . (-69) . . m 1998 AJHSME Problems/Problem 8 (→See also)
- 23:59, 9 June 2011 (diff | hist) . . (-68) . . m 1998 AJHSME Problems/Problem 9
- 23:59, 9 June 2011 (diff | hist) . . (-68) . . m 1998 AJHSME Problems/Problem 10
- 15:45, 6 June 2011 (diff | hist) . . (+332) . . 1998 AHSME Problems/Problem 5
- 15:43, 6 June 2011 (diff | hist) . . (+51) . . m 1998 AHSME Problems/Problem 1
- 15:42, 6 June 2011 (diff | hist) . . (+37) . . m 1998 AHSME Problems/Problem 10
- 14:10, 6 June 2011 (diff | hist) . . (+702) . . N 2010 USAMO Problems/Problem 6 (Created page with "== Problem == A blackboard contains 68 pairs of nonzero integers. Suppose that for each positive integer <math>k</math> at most one of the pairs <math>(k, k)</math> and <math>(-...")
- 14:04, 6 June 2011 (diff | hist) . . (+603) . . N 2011 USAMO Problems/Problem 5 (Created page with "==Problem== Let <math>P</math> be a given point inside quadrilateral <math>ABCD</math>. Points <math>Q_1</math> and <math>Q_2</math> are located within <math>ABCD</math> such th...")
- 00:08, 6 June 2011 (diff | hist) . . (+1,076) . . 2006 Romanian NMO Problems/Grade 8/Problem 2 (current)
- 20:17, 5 June 2011 (diff | hist) . . (-14) . . m 1999 AHSME Problems/Problem 15 (→Solution)
- 20:17, 5 June 2011 (diff | hist) . . (+135) . . 1999 AHSME Problems/Problem 15
- 17:24, 5 June 2011 (diff | hist) . . (+153) . . m 2011 AMC 10B Problems/Problem 20
- 17:21, 5 June 2011 (diff | hist) . . (-530) . . 2011 AMC 12B Problems/Problem 16 (Redirected page to 2011 AMC 10B Problems/Problem 20) (current)
- 17:18, 5 June 2011 (diff | hist) . . (+457) . . N 2011 AMC 12B Problems/Problem 10 (Created page with "==Problem== Rectangle <math>ABCD</math> has <math>AB=6</math> and <math>BC=3</math>. Point <math>M</math> is chosen on side <math>AB</math> so that <math>\angle AMD=\angle CMD</m...")
- 17:16, 5 June 2011 (diff | hist) . . (+552) . . N 2011 AMC 12B Problems/Problem 12 (Created page with "==Problem== A dart board is a regular octagon divided into regions as shown below. Suppose that a dart thrown at the board is equally likely to land anywhere on the board. What i...")
- 17:15, 5 June 2011 (diff | hist) . . (+479) . . N 2011 AMC 12B Problems/Problem 13 (Created page with "==Problem== Brian writes down four integers <math>w > x > y > z</math> whose sum is <math>44</math>. The pairwise positive differences of these numbers are <math>1, 3, 4, 5, 6</m...")
- 17:14, 5 June 2011 (diff | hist) . . (-3) . . m 2011 AMC 12B Problems/Problem 14 (→Problem 15)
- 17:12, 5 June 2011 (diff | hist) . . (+553) . . N 2011 AMC 12B Problems/Problem 14 (Created page with "==Problem 15== A segment through the focus <math>F</math> of a parabola with vertex <math>V</math> is perpendicular to <math>\overline{FV}</math> and intersects the parabola in p...")
- 17:11, 5 June 2011 (diff | hist) . . (+576) . . N 2011 AMC 12B Problems/Problem 16 (Created page with "==Problem== Rhombus <math>ABCD</math> has side length <math>2</math> and <math>\angle B = 120^{\circ}</math>. Region <math>R</math> consists of all points inside of the rhombus t...")
- 17:02, 5 June 2011 (diff | hist) . . (-2,003) . . 2011 AMC 10B Problems/Problem 20
- 13:18, 3 June 2011 (diff | hist) . . (+249) . . 1958 AHSME Problems/Problem 3
- 13:08, 3 June 2011 (diff | hist) . . (+14) . . m 2005 AMC 12B Problems/Problem 23 (→Solution)
- 01:15, 3 June 2011 (diff | hist) . . (-9) . . m 2010 AMC 12B Problems/Problem 10
- 01:13, 3 June 2011 (diff | hist) . . (+994) . . m Angle Bisector Theorem
- 00:52, 3 June 2011 (diff | hist) . . (+90) . . m Asymptote: 3D graphics
- 23:49, 2 June 2011 (diff | hist) . . (+19) . . m Asymptote: 3D graphics
- 23:44, 2 June 2011 (diff | hist) . . (+25) . . m 2001 AMC 10 Problems/Problem 10
- 23:34, 2 June 2011 (diff | hist) . . (+8) . . m 1990 AIME Problems/Problem 15 (→Solution 2)
- 23:32, 2 June 2011 (diff | hist) . . (+315) . . N Linear recurrence (Created page with 'A sequence <math>\{a_{0},a_{1},a_{2},\ldots\}</math> is said to obey a '''linear recurrence of order <math>k</math>''' if there exist constants <math>c_{0},c_{1},\ldots,c_{k-1}</…') (current)
- 23:24, 2 June 2011 (diff | hist) . . (-5) . . m Angle Bisector Theorem
- 18:47, 1 June 2011 (diff | hist) . . (+79) . . m Law of Sines (→Method 2)
- 18:45, 1 June 2011 (diff | hist) . . (+448) . . Law of Sines (→Method 1)
- 18:27, 1 June 2011 (diff | hist) . . (+1,960) . . N 2008 AMC 12B Problems/Problem 15 (Created page with '==Problem== On each side of a unit square, an equilateral triangle of side length 1 is constructed. On each new side of each equilateral triangle, another equilateral triangle of…')
- 18:06, 1 June 2011 (diff | hist) . . (+23) . . m 2008 AMC 12B Problems/Problem 19
- 01:15, 8 August 2010 (diff | hist) . . (+354) . . m 2002 AIME I Problems/Problem 15
- 23:29, 7 August 2010 (diff | hist) . . (+532) . . m 2007 AMC 10A Problems/Problem 21 (→Solution 1)
- 22:45, 7 August 2010 (diff | hist) . . (+17) . . m Asymptote: Basics (→Variables and Data Types)
- 19:13, 7 August 2010 (diff | hist) . . (+34) . . m Asymptote (Vector Graphics Language)
- 17:22, 7 August 2010 (diff | hist) . . (+538) . . m 2009 AIME I Problems/Problem 5 (→Solution)
- 16:03, 7 August 2010 (diff | hist) . . (+9) . . m Asymptote (Vector Graphics Language)
- 23:07, 6 August 2010 (diff | hist) . . (+32) . . m 2010 IMO Problems/Problem 4 (→Solution 1)
- 22:59, 6 August 2010 (diff | hist) . . (+461) . . m 1998 AHSME Problems
- 19:26, 30 June 2010 (diff | hist) . . (-43) . . m Mathematics scholarships (Reverted edits by Enrikem (Talk) to last revision by Vicky13)
- 08:35, 22 July 2009 (diff | hist) . . (+735) . . N 2009 USAMO Problems/Problem 6 (Created page with '== Problem == Let <math>s_1, s_2, s_3, \ldots</math> be an infinite, nonconstant sequence of rational numbers, meaning it is not the case that <math>s_1 = s_2 = s_3 = \cdots.</ma…')
- 08:34, 22 July 2009 (diff | hist) . . (+791) . . N 2009 USAMO Problems/Problem 5 (Created page with '== Problem == Trapezoid <math>ABCD</math>, with <math>\overline{AB}||\overline{CD}</math>, is inscribed in circle <math>\omega</math> and point <math>G</math> lies inside triangl…')
- 08:30, 22 July 2009 (diff | hist) . . (+984) . . Orthocenter
- 06:50, 22 July 2009 (diff | hist) . . (0) . . m Number theory (→Books)
- 00:58, 27 March 2009 (diff | hist) . . (+1,470) . . m Derivative/Formulas (Reverted edits by Mathforce1 (Talk) to last version by 1=2)
- 13:26, 13 March 2009 (diff | hist) . . (0) . . m 1987 AIME Answer Key (current)
- 21:15, 9 March 2009 (diff | hist) . . (+1,021) . . m Floor function
- 11:51, 28 February 2009 (diff | hist) . . (+429) . . m 1984 AIME Problems/Problem 15 (→Solution)
- 10:35, 28 February 2009 (diff | hist) . . (-1) . . m 1984 AIME Problems (→Problem 8)
- 23:52, 11 February 2009 (diff | hist) . . (-120) . . m United States of America Mathematical Olympiad (→Recommended reading)
- 01:24, 5 January 2009 (diff | hist) . . (+13) . . m 2006 AIME A Problems/Problem 15 (→Solution)
- 03:25, 4 January 2009 (diff | hist) . . (-54) . . m Template:ProbAMC (current)
- 22:35, 3 January 2009 (diff | hist) . . (+3,015) . . 1975 USAMO Problems/Problem 2
- 17:08, 3 January 2009 (diff | hist) . . (+3,160) . . N 1976 USAMO Problems (New page: Problems from the '''1976 USAMO'''. ==Problem 1== <asy> void fillsq(int x, int y){ fill((x,y)--(x+1,y)--(x+1,y+1)--(x,y+1)--cycle, ...)
- 17:06, 3 January 2009 (diff | hist) . . (+4) . . m 1975 USAMO Problems
- 17:04, 3 January 2009 (diff | hist) . . (+26) . . m 1976 USAMO Problems/Problem 5
- 17:03, 3 January 2009 (diff | hist) . . (+377) . . N 1976 USAMO Problems/Problem 4 (New page: ==Problem== If the sum of the lengths of the six edges of a trirectangular tetrahedron <math>PABC</math> (i.e., <math>\angle APB=\angle BPC=\angle CPA=90^o</math>) is <math>S</math>, deter...)
- 16:57, 3 January 2009 (diff | hist) . . (+363) . . m 1994 AIME Problems/Problem 6 (→Solution)
- 16:41, 3 January 2009 (diff | hist) . . (+15) . . m 1994 AIME Problems/Problem 14 (→Solution)
- 16:41, 3 January 2009 (diff | hist) . . (+1,270) . . N 1976 USAMO Problems/Problem 2 (New page: ==Problem== If <math>A</math> and <math>B</math> are fixed points on a given circle and <math>XY</math> is a variable diameter of the same circle, determine the locus of the point of inter...)
- 14:43, 3 January 2009 (diff | hist) . . (+438) . . m 1976 USAMO Problems/Problem 1
- 02:20, 3 January 2009 (diff | hist) . . (+1,128) . . m AoPS Wiki:AoPS Community Awards (→Perfect AMC Scores)
- 01:47, 3 January 2009 (diff | hist) . . (+1,220) . . 1974 USAMO Problems/Problem 2
- 01:15, 3 January 2009 (diff | hist) . . (+3,278) . . 1974 USAMO Problems/Problem 5
- 22:52, 2 January 2009 (diff | hist) . . (0) . . m Template:AIME Problems
- 21:29, 31 December 2008 (diff | hist) . . (+16) . . m USAMO Problems and Solutions
- 18:36, 30 December 2008 (diff | hist) . . (-3) . . m 1973 USAMO Problems (→See also)
- 18:36, 30 December 2008 (diff | hist) . . (-3) . . m 1974 USAMO Problems (→See also)
- 18:36, 30 December 2008 (diff | hist) . . (+2,098) . . N 1975 USAMO Problems (New page: Problems from the ''' USAMO'''. ==Problem 1== (a) Prove that <center><math>[5x]+[5y]\ge [3x+y]+[3y+x]</math>,</center> where <math>x,y...)
- 18:33, 30 December 2008 (diff | hist) . . (+1) . . m 1975 USAMO Problems/Problem 1 (→Problem)
- 18:32, 30 December 2008 (diff | hist) . . (+487) . . N 1975 USAMO Problems/Problem 5 (New page: ==Problem== A deck of <math>n</math> playing cards, which contains three aces, is shuffled at random (it is assumed that all possible card distributions are equally likely). The cards are ...)
- 18:28, 30 December 2008 (diff | hist) . . (+2,181) . . N 1963 IMO Problems (New page: Problems of the 5th IMO 1963 Poland. == Day I == === Problem 1 === Find all real roots of the equation <center><math>\sqrt{x^2-p}+2\sqrt{x^2-1}=x</math>,</center>where <math>p</math...)
- 18:25, 30 December 2008 (diff | hist) . . (+732) . . N 1963 IMO Problems/Problem 6 (New page: ==Problem== Five students, <math>A,B,C,D,E</math>, took part in a contest. One prediction was that the contestants would finish in the order <math>ABCDE</math>. This prediction was very po...)
- 18:23, 30 December 2008 (diff | hist) . . (+190) . . N 1963 IMO Problems/Problem 5 (New page: ==Problem== Prove that <math>\cos{\frac{\pi}{7}}-\cos{\frac{2\pi}{7}}+\cos{\frac{3\pi}{7}}=\frac{1}{2}</math>. ==Solution== {{solution}} ==See Also== {{IMO box|year=1963|num-b=4|num-a=6...)
- 18:21, 30 December 2008 (diff | hist) . . (+339) . . N 1963 IMO Problems/Problem 4 (New page: ==Problem== Find all solutions <math>x_1,x_2,x_3,x_4,x_5</math> of the system <center><math>\begin{eqnarray} x_5+x_2&=&yx_1\\ x_1+x_3&=&yx_2\\ x_2+x_4&=&yx_3\\ x_3+x_5&=&yx_4\\ x_4+x_1&=&y...)
- 18:19, 30 December 2008 (diff | hist) . . (+316) . . N 1963 IMO Problems/Problem 3 (New page: ==Problem== In an <math>n</math>-gon all of whose interior angles are equal, the lengths of consecutive sides satisfy the relation <center><math>a_1\ge a_2\ge \cdots \ge a_n</math>.</cente...)
- 18:17, 30 December 2008 (diff | hist) . . (+336) . . N 1963 IMO Problems/Problem 2 (New page: ==Problem== Point <math>A</math> and segment <math>BC</math> are given. Determine the locus of points in space which are the vertices of right angles with one side passing through <math>A<...)
- 18:15, 30 December 2008 (diff | hist) . . (+243) . . N 1963 IMO Problems/Problem 1 (New page: ==Problem== Find all real roots of the equation <center><math>\sqrt{x^2-p}+2\sqrt{x^2-1}=x</math>,</center>where <math>p</math> is a real parameter. ==Solution== {{solution}} ==See Also...)
- 18:10, 30 December 2008 (diff | hist) . . (+422) . . N 1962 IMO Problems/Problem 7 (New page: ==Problem== The tetrahedron <math>SABC</math> has the following property: there exist five spheres, each tangent to the edges <math>SA, SB, SC, BC, CA, AB</math>, or to their extensions. ...)
- 18:09, 30 December 2008 (diff | hist) . . (+374) . . N 1962 IMO Problems/Problem 6 (New page: ==Problem== Consider an isosceles triangle. Let <math>r</math> be the radius of its circumscribed circle and <math>\rho</math> the radius of its inscribed circle. Prove that the distance <...)
- 18:09, 30 December 2008 (diff | hist) . . (+346) . . N 1962 IMO Problems/Problem 5 (New page: ==Problem== On the circle <math>K</math> there are given three distinct points <math>A,B,C</math>. Construct (using only straightedge and compass) a fourth point <math>D</math> on <math>K<...)
- 18:08, 30 December 2008 (diff | hist) . . (+155) . . N 1962 IMO Problems/Problem 4 (New page: ==Problem== Solve the equation <math>cos^2{x}+cos^2{2x}+cos^2{3x}=1</math>. ==Solution== {{solution}} ==See Also== {{IMO box|year=1962|num-b=3|num-a=5}})
- 18:08, 30 December 2008 (diff | hist) . . (+841) . . N 1962 IMO Problems/Problem 3 (New page: ==Problem== Consider the cube <math>ABCDA'B'C'D'</math>(<math>ABCD</math> and <math>A'B'C'D'</math> are the upper and lower bases, respectively, and edges <math>AA'</math>, <math>BB'</math...)
- 18:07, 30 December 2008 (diff | hist) . . (+238) . . N 1962 IMO Problems/Problem 2 (New page: ==Problem== Determine all real numbers <math>x</math> which satisfy the inequality: <center> <math>\sqrt{\sqrt{3-x}-\sqrt{x+1}}>\dfrac{1}{2}</math> </center> ==Solution== {{solution}} =...)
- 17:57, 30 December 2008 (diff | hist) . . (+409) . . N 1962 IMO Problems/Problem 1 (New page: ==Problem== Find the smallest natural number <math>n</math> which has the following properties: (a) Its decimal representation has 6 as the last digit. (b) If the last digit 6 is erased ...)
- 17:56, 30 December 2008 (diff | hist) . . (-2) . . m 1962 IMO Problems (→Problem 1)
- 17:55, 30 December 2008 (diff | hist) . . (+1,325) . . 1962 IMO Problems
- 17:46, 30 December 2008 (diff | hist) . . (+587) . . N 1960 IMO Problems/Problem 7 (New page: ==Problem== An isosceles trapezoid with bases <math>a</math> and <math>c</math> and altitude <math>h</math> is given. a) On the axis of symmetry of this trapezoid, find all points <math>P...)
- 17:45, 30 December 2008 (diff | hist) . . (-13) . . m 1960 IMO Problems/Problem 6 (→See Also)
- 17:18, 30 December 2008 (diff | hist) . . (+664) . . N 1975 USAMO Problems/Problem 4 (New page: ==Problem== Two given circles intersect in two points <math>P</math> and <math>Q</math>. Show how to construct a segment <math>AB</math> passing through <math>P</math> and terminating on t...)
- 17:12, 30 December 2008 (diff | hist) . . (+302) . . N 1975 USAMO Problems/Problem 3 (New page: ==Problem== If <math>P(x)</math> denotes a polynomial of degree <math>n</math> such that <math>P(k)=k/(k+1)</math> for <math>k=0,1,2,\ldots,n</math>, determine <math>P(n+1)</math>. ==Solu...)
- 17:11, 30 December 2008 (diff | hist) . . (+390) . . N 1975 USAMO Problems/Problem 2 (New page: ==Problem== Let <math>A,B,C,D</math> denote four points in space and <math>AB</math> the distance between <math>A</math> and <math>B</math>, and so on. Show that <center><math>AC^2+BD^2+AD...)
- 17:09, 30 December 2008 (diff | hist) . . (+538) . . N 1975 USAMO Problems/Problem 1 (New page: ==Problem== (a) Prove that <center><math>[5x]+[5y]\ge [3x+y]+[3y+x]</math>,</center>where <math>x,y\ge 0</math> and <math>[u]</math> denotes the greatest integer <math>\le u</math> (e.g., ...)
- 17:04, 30 December 2008 (diff | hist) . . (+427) . . N 1975 USAMO (New page: The '''Fourth USAMO''' was held May 6, 1975. There were five problems. * 1975 USAMO Problems * Problem 1 * [[1975 USAMO Problems/Problem 2 | P...)
- 17:02, 30 December 2008 (diff | hist) . . (+2,660) . . N 1974 USAMO Problems (New page: Problems from the '''1974 USAMO'''. ==Problem 1== Let <math>a</math>, <math>b</math>, and <math>c</math> denote three distinct integer...)
- 17:00, 30 December 2008 (diff | hist) . . (-12) . . m 1974 USAMO Problems/Problem 4 (→See also)
- 17:00, 30 December 2008 (diff | hist) . . (+774) . . N 1974 USAMO Problems/Problem 4 (New page: ==Problem== A father, mother and son hold a family tournament, playing a two person board game with no ties. The tournament rules are: (i) The weakest player chooses the first two contest...)
- 16:56, 30 December 2008 (diff | hist) . . (+336) . . N 1974 USAMO Problems/Problem 3 (New page: ==Problem== Two boundary points of a ball of radius 1 are joined by a curve contained in the ball and having length less than 2. Prove that the curve is contained entirely within some hemi...)
- 16:54, 30 December 2008 (diff | hist) . . (+294) . . N 1974 USAMO Problems/Problem 2 (New page: ==Problem== Prove that if <math>a</math>, <math>b</math>, and <math>c</math> are positive real numbers, then <center><math>a^ab^bc^c\ge (abc)^{(a+b+c)/3}</math></center> ==Solution== {{so...)
- 15:58, 30 December 2008 (diff | hist) . . (-3) . . m 1972 USAMO Problems (→See also)
- 15:57, 30 December 2008 (diff | hist) . . (+2,293) . . N 1972 USAMO Problems (New page: Problems from the '''1972 USAMO'''. ==Problem 1== The symbols <math>(a,b,\ldots,g)</math> and <math>[a,b,\ldots, g]</math> denote the ...)
- 15:52, 30 December 2008 (diff | hist) . . (+4) . . m 1972 USAMO Problems/Problem 5 (→See also)
- 15:52, 30 December 2008 (diff | hist) . . (+21) . . m 1972 USAMO Problems/Problem 5 (→See also)
- 15:52, 30 December 2008 (diff | hist) . . (+805) . . N 1972 USAMO Problems/Problem 5 (New page: ==Problem== A given convex pentagon <math>ABCDE</math> has the property that the area of each of the five triangles <math>ABC</math>, <math>BCD</math>, <math>CDE</math>, <math>DEA</math>, ...)
- 15:42, 30 December 2008 (diff | hist) . . (+404) . . N 1972 USAMO Problems/Problem 4 (New page: ==Problem== Let <math>R</math> denote a non-negative rational number. Determine a fixed set of integers <math>a,b,c,d,e,f</math>, such that for ''every'' choice of <math>R</math>, <center...)
- 15:39, 30 December 2008 (diff | hist) . . (+530) . . N 1972 USAMO Problems/Problem 1 (New page: ==Problem== The symbols <math>(a,b,\ldots,g)</math> and <math>[a,b,\ldots, g]</math> denote the greatest common divisor and least common multiple, respectively, of the positive integers <m...)
- 15:35, 30 December 2008 (diff | hist) . . (+296) . . N 1972 USAMO Problems/Problem 2 (New page: ==Problem== A given tetrahedron <math>ABCD</math> is isosceles, that is, <math>AB=CD, AC=BD, AD=BC</math>. Show that the faces of the tetrahedron are acute-angled triangles. ==Solution== ...)
- 15:33, 30 December 2008 (diff | hist) . . (0) . . m 1972 USAMO Problems/Problem 3 (→See also)
- 15:33, 30 December 2008 (diff | hist) . . (0) . . m 1972 USAMO Problems/Problem 3 (→See also)
- 15:31, 30 December 2008 (diff | hist) . . (+1,897) . . N 1973 USAMO Problems (New page: Problems from the '''1973 USAMO'''. ==Problem 1== Two points <math>P</math> and <math>Q</math> lie in the interior of a regular tetrah...)
- 15:26, 30 December 2008 (diff | hist) . . (+41) . . m 1973 USAMO Problems/Problem 5 (→Problem)
- 15:24, 30 December 2008 (diff | hist) . . (+443) . . N 1973 USAMO Problems/Problem 3 (New page: ==Problem== Three distinct vertices are chosen at random from the vertices of a given regular polygon of <math>(2n+1)</math> sides. If all such choices are equally likely, what is the prob...)
- 15:22, 30 December 2008 (diff | hist) . . (+13) . . m 1973 USAMO Problems/Problem 1 (→Solution)
- 15:21, 30 December 2008 (diff | hist) . . (+284) . . N 1973 USAMO Problems/Problem 1 (New page: ==Problem== Two points <math>P</math> and <math>Q</math> lie in the interior of a regular tetrahedron <math>ABCD</math>. Prove that angle <math>PAQ<60^o</math>. ==Solution== ==See also==...)
- 15:18, 30 December 2008 (diff | hist) . . (-152) . . m 1973 USAMO Problems/Problem 2 (→Problem)
- 02:46, 21 December 2008 (diff | hist) . . (+2,829) . . N 2001 USAMO Problems (New page: Problems of the 2001 USAMO. == Day 1 == === Problem 1 === Each of eight boxes contains six balls. Each ball has been colored with one of <math>n</math> colors, such...)
- 02:42, 21 December 2008 (diff | hist) . . (-45) . . m 2002 USAMO Problems/Problem 3 (→Problem)
- 02:42, 21 December 2008 (diff | hist) . . (0) . . m 2002 USAMO Problems (→Problem 3)
- 02:40, 21 December 2008 (diff | hist) . . (+423) . . N 2001 USAMO Problems/Problem 6 (New page: == Problem == Each point in the plane is assigned a real number such that, for any triangle, the number at the center of its inscribed circle is equal to the arithmetic mean of the three ...)
- 02:38, 21 December 2008 (diff | hist) . . (+523) . . N 2001 USAMO Problems/Problem 5 (New page: == Problem == Let <math>S</math> be a set of integers (not necessarily positive) such that (a) there exist <math>a,b \in S</math> with <math>\gcd(a,b) = \gcd(a - 2,b - 2) = 1</math>; (b...)
- 02:37, 21 December 2008 (diff | hist) . . (+4) . . 2001 USAMO Problems/Problem 4
- 02:36, 21 December 2008 (diff | hist) . . (+463) . . N 2001 USAMO Problems/Problem 4 (New page: == Problem == Let <math>P</math> be a point in the plane of triangle <math>ABC</math> such that the segments <math>PA</math>, <math>PB</math>, and <math>PC</math> are the sides of an obtu...)
- 02:35, 21 December 2008 (diff | hist) . . (+312) . . N 2001 USAMO Problems/Problem 3 (New page: == Problem == Let <math>a, b, c \geq 0</math> and satisfy <center><math>a^2 + b^2 + c^2 + abc = 4.</math></center> Show that <center><math>ab + bc + ca - abc \leq 2.</math></center> == So...)
- 02:29, 21 December 2008 (diff | hist) . . (+3,035) . . N 2002 USAMO Problems (New page: Problems of the 2002 USAMO. == Day 1 == === Problem 1 === Let <math>S </math> be a set with 2002 elements, and let <math>N </math> be an integer with <math> 0 \le N...)
- 02:19, 21 December 2008 (diff | hist) . . (+6) . . m 2002 USAMO Problems/Problem 6
- 02:18, 21 December 2008 (diff | hist) . . (+809) . . N 2002 USAMO Problems/Problem 6 (New page: == Problem == I have an <math>n \times n</math> sheet of stamps, from which I've been asked to tear out blocks of three adjacent stamps in a single row or column. (I can only tear along t...)
- 19:58, 18 December 2008 (diff | hist) . . (+801) . . 2003 USAMO Problems/Problem 5
- 19:54, 18 December 2008 (diff | hist) . . (+598) . . 2003 USAMO Problems/Problem 4
- 19:40, 18 December 2008 (diff | hist) . . (+4,499) . . 2003 USAMO Problems/Problem 6
- 18:43, 18 December 2008 (diff | hist) . . (+495) . . m Cauchy-Schwarz Inequality (→Introductory)
- 19:01, 20 August 2008 (diff | hist) . . (+354) . . N 2001 IMO Shortlist Problems/N6 (New page: == Problem == Is it possible to find 100 positive integers not exceeding 25,000, such that all pairwise sums of them are different? == Solution == {{solution}} == Resources == * [[2001 ...)
- 18:59, 20 August 2008 (diff | hist) . . (+423) . . N 2001 IMO Shortlist Problems/N5 (New page: == Problem == Let <math>a > b > c > d</math> be positive integers and suppose that <center><math>ac + bd = (b + d + a - c)(b + d - a + c).</math></center> Prove that <math>ab + cd</math> i...)
- 18:57, 20 August 2008 (diff | hist) . . (+485) . . N 2001 IMO Shortlist Problems/N4 (New page: == Problem == Let <math>p \geq 5</math> be a prime number. Prove that there exists an integer <math>a</math> with <math>1 \leq a \leq p - 2</math> such that neither <math>a^{p - 1} - 1</ma...)
- 18:56, 20 August 2008 (diff | hist) . . (+424) . . N 2001 IMO Shortlist Problems/N3 (New page: == Problem == Let <math>a_1 = 11^{11}, \, a_2 = 12^{12}, \, a_3 = 13^{13}</math>, and <math>a_n = |a_{n - 1} - a_{n - 2}| + |a_{n - 2} - a_{n - 3}|, n \geq 4.</math> Determine <math>a_{14^...) (current)
- 18:55, 20 August 2008 (diff | hist) . . (+503) . . N 2001 IMO Shortlist Problems/N2 (New page: == Problem == Consider the system <math>x + y = z + u,</math> <math>2xy & = zu.</math> Find the greatest value of the real constant <math>m</math> such that <math>m \leq x/y</math> for any...)
- 18:54, 20 August 2008 (diff | hist) . . (+426) . . N 2001 IMO Shortlist Problems/N1 (New page: == Problem == Prove that there is no positive integer <math>n</math> such that, for <math>k = 1,2,\ldots,9</math>, the leftmost digit (in decimal notation) of <math>(n + k)!</math> equals ...)
- 18:51, 20 August 2008 (diff | hist) . . (+567) . . N 2001 IMO Shortlist Problems/G8 (New page: == Problem == Let <math>ABC</math> be a triangle with <math>\angle BAC = 60^{\circ}</math>. Let <math>AP</math> bisect <math>\angle BAC</math> and let <math>BQ</math> bisect <math>\angle ...)
- 18:50, 20 August 2008 (diff | hist) . . (+726) . . N 2001 IMO Shortlist Problems/G7 (New page: == Problem == Let <math>O</math> be an interior point of acute triangle <math>ABC</math>. Let <math>A_1</math> lie on <math>BC</math> with <math>OA_1</math> perpendicular to <math>BC</math...) (current)
- 18:49, 20 August 2008 (diff | hist) . . (+756) . . N 2001 IMO Shortlist Problems/G6 (New page: == Problem == Let <math>ABC</math> be a triangle and <math>P</math> an exterior point in the plane of the triangle. Suppose the lines <math>AP</math>, <math>BP</math>, <math>CP</math> meet...)
- 18:47, 20 August 2008 (diff | hist) . . (+944) . . N 2001 IMO Shortlist Problems/G5 (New page: == Problem == Let <math>ABC</math> be an acute triangle. Let <math>DAC,EAB</math>, and <math>FBC</math> be isosceles triangles exterior to <math>ABC</math>, with <math>DA = DC, EA = EB</m...) (current)
- 18:46, 20 August 2008 (diff | hist) . . (+831) . . N 2001 IMO Shortlist Problems/G4 (New page: == Problem == Let <math>M</math> be a point in the interior of triangle <math>ABC</math>. Let <math>A'</math> lie on <math>BC</math> with <math>MA'</math> perpendicular to <math>BC</math>....) (current)
- 18:44, 20 August 2008 (diff | hist) . . (+551) . . N 2001 IMO Shortlist Problems/G3 (New page: == Problem == Let <math>ABC</math> be a triangle with centroid <math>G</math>. Determine, with proof, the position of the point <math>P</math> in the plane of <math>ABC</math> such that <m...)
- 18:43, 20 August 2008 (diff | hist) . . (+594) . . N 2001 IMO Shortlist Problems/G2 (New page: == Problem == Consider an acute-angled triangle <math>ABC</math>. Let <math>P</math> be the foot of the altitude of triangle <math>ABC</math> issuing from the vertex <math>A</math>, and le...)
- 18:39, 20 August 2008 (diff | hist) . . (+724) . . N 2001 IMO Shortlist Problems/G1 (New page: == Problem == Let <math>A_1</math> be the center of the square inscribed in acute triangle <math>ABC</math> with two vertices of the square on side <math>BC</math>. Thus one of the two re...)
- 18:36, 20 August 2008 (diff | hist) . . (+588) . . N 2001 IMO Shortlist Problems/C8 (New page: == Problem == Twenty-one girls and twenty-one boys took part in a mathematical competition. It turned out that each contestant solved at most six problems, and for each pair of a girl and ...) (current)
- 18:36, 20 August 2008 (diff | hist) . . (+991) . . N 2001 IMO Shortlist Problems/C7 (New page: == Problem == A pile of <math>n</math> pebbles is placed in a vertical column. This configuration is modified according to the following rules. A pebble can be moved if it is at the top of...)
- 18:34, 20 August 2008 (diff | hist) . . (0) . . m 2001 IMO Shortlist Problems/C6 (corrected consequences of mindless copying and pasting :P) (current)
- 18:33, 20 August 2008 (diff | hist) . . (+1,061) . . N 2001 IMO Shortlist Problems/C6 (New page: == Problem == For a positive integer <math>n</math> define a sequence of zeros and ones to be [i]balanced[/i] if it contains <math>n</math> zeros and <math>n</math> ones. Two balanced sequ...)
- 18:32, 20 August 2008 (diff | hist) . . (+448) . . Nm 2001 IMO Shortlist Problems/C5 (New page: == Problem == Find all finite sequences <math>(x_0, x_1, \ldots,x_n)</math> such that for every <math>j</math>, <math>0 \leq j \leq n</math>, <math>x_j</math> equals the number of times <m...)
- 18:26, 20 August 2008 (diff | hist) . . (+606) . . m 2001 IMO Shortlist Problems/A1
- 18:23, 20 August 2008 (diff | hist) . . (+509) . . Nm 2001 IMO Shortlist Problems/C4 (New page: == Problem == A set of three nonnegative integers <math>\{x,y,z\}</math> with <math>x < y < z</math> is called <i>historic</i> if <math>\{z - y,y - x\} = \{1776,2001\}</math>. Show that t...)
- 18:21, 20 August 2008 (diff | hist) . . (+579) . . Nm 2001 IMO Shortlist Problems/C3 (New page: == Problem == Define a <math>k</math>-<i>clique</i> to be a set of <math>k</math> people such that every pair of them are acquainted with each other. At a certain party, every pair of 3-cl...)
- 18:19, 20 August 2008 (diff | hist) . . (+650) . . Nm 2001 IMO Shortlist Problems/C2 (New page: == Problem == Let <math>n</math> be an odd integer greater than 1 and let <math>c_1, c_2, \ldots, c_n</math> be integers. For each permutation <math>a = (a_1, a_2, \ldots, a_n)</math> of <...)
- 18:17, 20 August 2008 (diff | hist) . . (+462) . . Nm 2001 IMO Shortlist Problems/A6 (New page: == Problem == Prove that for all positive real numbers <math>a,b,c</math>, <center><math>\frac {a}{\sqrt {a^2 + 8bc}} + \frac {b}{\sqrt {b^2 + 8ca}} + \frac {c}{\sqrt {c^2 + 8ab}} \geq 1.<...)
- 18:16, 20 August 2008 (diff | hist) . . (+549) . . Nm 2001 IMO Shortlist Problems/A5 (New page: == Problem == Find all positive integers <math>a_1, a_2, \ldots, a_n</math> such that <center><math>\frac {99}{100} = \frac {a_0}{a_1} + \frac {a_1}{a_2} + \cdots + \frac {a_{n - 1}}{a_n},...)
- 18:14, 20 August 2008 (diff | hist) . . (+445) . . Nm 2001 IMO Shortlist Problems/A4 (New page: == Problem == Find all functions <math>f: \mathbb{R} \rightarrow \mathbb{R}</math>, satisfying <center><math>f(xy)(f(x) - f(y)) = (x - y)f(x)f(y)</math></center> for all <math>x,y</math>. ...)
- 18:13, 20 August 2008 (diff | hist) . . (+61) . . Nm Category:Functional Equation (New page: This page lists all the functional equations in the AopsWiki.) (current)
- 18:06, 20 August 2008 (diff | hist) . . (+505) . . Nm 2001 IMO Shortlist Problems/A2 (New page: == Problem == Let <math>a_0, a_1, a_2, \ldots</math> be an arbitrary infinite sequence of positive numbers. Show that the inequality <math>1 + a_n > a_{n - 1} \sqrt [n]{2}</math> holds fo...)
- 18:01, 20 August 2008 (diff | hist) . . (+42) . . m 1999 IMO Problems/Problem 2
- 18:00, 20 August 2008 (diff | hist) . . (+42) . . m 2001 IMO Shortlist Problems/A3
- 17:59, 20 August 2008 (diff | hist) . . (+42) . . m 2004 USAMO Problems/Problem 5
- 17:59, 20 August 2008 (diff | hist) . . (-166) . . m 2002 USAMO Problems/Problem 2
- 17:58, 20 August 2008 (diff | hist) . . (-414) . . m 2002 IMO Shortlist Problems/A2 (current)
- 17:56, 20 August 2008 (diff | hist) . . (+1,087) . . 2003 USAMO Problems (→Day 2)
- 17:55, 20 August 2008 (diff | hist) . . (+635) . . N 2003 USAMO Problems/Problem 6 (New page: == Problem == At the vertices of a regular hexagon are written six nonnegative integers whose sum is 2003. Bert is allowed to make moves of the following form: he may pick a vertex and re...)
- 17:53, 20 August 2008 (diff | hist) . . (+478) . . N 2003 USAMO Problems/Problem 5 (New page: == Problem == Let <math>a</math>, <math>b</math>, <math>c</math> be positive real numbers. Prove that <center><math>\dfrac{(2a + b + c)^2}{2a^2 + (b + c)^2} + \dfrac{(2b + c + a)^2}{2b^2 ...)
- 17:49, 20 August 2008 (diff | hist) . . (+654) . . N 2003 USAMO Problems/Problem 4 (New page: == Problem == Let <math>ABC</math> be a triangle. A circle passing through <math>A</math> and <math>B</math> intersects segments <math>AC</math> and <math>BC</math> at <math>D</math> and ...)
- 19:53, 22 July 2008 (diff | hist) . . (+1) . . m Chicago ARML
- 22:16, 17 July 2008 (diff | hist) . . (-106) . . m 1989 AIME Problems/Problem 15
- 22:14, 17 July 2008 (diff | hist) . . (-87) . . m 1989 AIME Problems/Problem 14
- 22:12, 17 July 2008 (diff | hist) . . (-36) . . m 1989 AIME Problems/Problem 13
- 22:12, 17 July 2008 (diff | hist) . . (-63) . . m 1989 AIME Problems/Problem 12
- 22:11, 17 July 2008 (diff | hist) . . (-30) . . m 1989 AIME Problems/Problem 11
- 22:10, 17 July 2008 (diff | hist) . . (-42) . . m 1989 AIME Problems/Problem 10
- 22:10, 17 July 2008 (diff | hist) . . (-9) . . m 1989 AIME Problems/Problem 9
- 22:09, 17 July 2008 (diff | hist) . . (-21) . . m 1989 AIME Problems/Problem 8
- 22:09, 17 July 2008 (diff | hist) . . (-170) . . m 1989 AIME Problems/Problem 7
- 22:09, 17 July 2008 (diff | hist) . . (-30) . . m 1989 AIME Problems/Problem 5
- 22:07, 17 July 2008 (diff | hist) . . (-24) . . m 1989 AIME Problems/Problem 4
- 22:06, 17 July 2008 (diff | hist) . . (-66) . . m 1989 AIME Problems/Problem 6
- 23:05, 8 July 2008 (diff | hist) . . (+3,897) . . m How should I prepare? (:D you guys can add more)
- 22:55, 8 July 2008 (diff | hist) . . (+87) . . m How should I prepare? (→Cheat Sheets)
- 12:57, 7 July 2008 (diff | hist) . . (+20) . . Nm Cevians (Redirecting to Cevian) (current)
- 12:56, 7 July 2008 (diff | hist) . . (+25) . . Nm Concurrency (Redirecting to Concurrence) (current)
- 23:10, 5 July 2008 (diff | hist) . . (+36) . . m 2006 AMC 10A Problems (→Problem 16)
- 23:09, 5 July 2008 (diff | hist) . . (+36) . . m 2006 AMC 10A Problems (→Problem 17)
- 23:07, 5 July 2008 (diff | hist) . . (+34) . . m 2006 AMC 12A Problems
- 23:07, 5 July 2008 (diff | hist) . . (+37) . . m 2006 AMC 12A Problems (→Problem 12)
- 23:05, 5 July 2008 (diff | hist) . . (+468) . . m 2008 AMC 10A Problems (→Problem 21)
- 23:03, 5 July 2008 (diff | hist) . . (+392) . . 2008 AMC 12A Problems/Problem 18 (→Solution)
- 22:45, 5 July 2008 (diff | hist) . . (+2,013) . . 2007 USAMO Problems/Problem 6
- 19:21, 5 July 2008 (diff | hist) . . (-10) . . m 2008 USAMO Problems/Problem 2 (→Solution 7 (inversion))
- 19:19, 5 July 2008 (diff | hist) . . (-26) . . m 2003 AIME I Problems/Problem 5
- 19:18, 5 July 2008 (diff | hist) . . (+325) . . m 1995 AHSME Problems/Problem 10 (→Solution)
- 17:22, 1 July 2008 (diff | hist) . . (+209) . . m
- 17:14, 1 July 2008 (diff | hist) . . (+33) . . Nm Holder inequality (Redirecting to Hölder's Inequality)
- 00:32, 6 June 2008 (diff | hist) . . (+330) . . m Math books (→Olympiad)
- 00:19, 6 June 2008 (diff | hist) . . (+116) . . m Math books (→Olympiad)
- 00:15, 6 June 2008 (diff | hist) . . (+75) . . m Math books (→Olympiad)
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