User contributions
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- 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)
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