MathDB

3.2

Part of 2011 Saudi Arabia Pre-TST

Problems(2)

any parallelogram can be dissected in n>=4 cyclic quadrilaterals.

Source: 2011 Saudi Arabia Pre-TST November 3.2 https://artofproblemsolving.com/community/c2745403_2011_

1/1/2022
Prove that for each n≥4n \ge 4 a parallelogram can be dissected in nn cyclic quadrilaterals.
combinatorial geometrygeometrycyclic quadrilateral
a+2b-b^2=\sqrt{2a+a^2+|2a+1-2b|}

Source: 2011 Saudi Arabia Pre-TST February 3.2

1/1/2022
Find all pairs of nonnegative integers (a,b)(a, b) such that a+2b−b2=2a+a2+∣2a+1−2b∣a+2b-b^2=\sqrt{2a+a^2+|2a+1-2b|}.
Diophantine equationdiophantinenumber theory