Art of Problem Solving

User contributions for Pureswag

A user with 113 edits. Account created on 16 October 2018.
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14 February 2021

11 February 2021

17 January 2021

10 January 2021

27 December 2020

23 August 2020

  • 11:2711:27, 23 August 2020 diff hist +388 N 2004 IMO Problems/Problem 5 Created page with "In a convex quadrilateral <math>ABCD</math>, the diagonal <math>BD</math> bisects neither the angle <math>ABC</math> nor the angle <math>CDA</math>. The point <math>P</math> l..."
  • 11:2611:26, 23 August 2020 diff hist +203 N 2004 IMO Problems/Problem 6 Created page with "We call a positive integer alternating if every two consecutive digits in its decimal representation are of different parity. Find all positive integers <math>n</math> which h..."
  • 11:2511:25, 23 August 2020 diff hist +259 N 2004 IMO Problems/Problem 3 Created page with "Define a “hook” to be a figure made up of six unit squares as shown in this picture: http://bit.ly/IMO2004P1, or any of the figures obtained by applying rotations and refl..."
  • 11:2111:21, 23 August 2020 diff hist +638 N 2005 IMO Problems/Problem 5 Created page with "Let <math>ABCD</math> be a fixed convex quadrilateral with <math>BC = DA</math> and <math>BC \nparallel DA</math>. Let two variable points <math>E</math> and <math>F</math> li..."
  • 11:1911:19, 23 August 2020 diff hist +346 N 2005 IMO Problems/Problem 2 Created page with "Let <math>a_1, a_2, \dots</math> be a sequence of integers with infinitely many positive and negative terms. Suppose that for every positive integer <math>n</math> the numbers..."
  • 11:1511:15, 23 August 2020 diff hist +180 N 2005 IMO Problems/Problem 3 Created page with "Let <math>x, y, z > 0</math> satisfy <math>xyz\ge 1</math>. Prove that <cmath>\frac{x^5-x^2}{x^5+y^2+z^2} + \frac{y^5-y^2}{x^2+y^5+z^2} + \frac{z^5-z^2}{x^2+y^2+z^5} \ge 0.</c..."
  • 11:0511:05, 23 August 2020 diff hist +432 N 2005 IMO Problems/Problem 1 Created page with "Six points are chosen on the sides of an equilateral triangle <math>ABC</math>: <math>A_1, A_2</math> on <math>BC</math>, <math>B_1</math>, <math>B_2</math> on <math>CA</math>..."

22 August 2020

16 August 2020

9 August 2020

22 June 2020

  • 15:3015:30, 22 June 2020 diff hist +650 N 2011 PuMAC Problems/NT Problem A8 Created page with "By multiplying both sides by 2 and simplifying, the condition becomes <math>(2a+1)^2 - 2b^2 = -1</math>. This is a variant of Pell's Equation <math>x^2 - 2y^2 = -1</math> with..." current
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