2016 IMO Problems/Problem 3

Revision as of 07:48, 25 May 2017 by Ekom2001 (talk | contribs) (Problem)


Let $P = A_1A_2 \cdots A_k$ be a convex polygon in the plane. The vertices $A_1,A_2,\dots, A_k$ have integral coordinates and lie on a circle. Let $S$ be the area of $P$. An odd positive integer $n$ is given such that the squares of the side lengths of $P$ are integers divisible by $n$. Prove that $2S$ is an integer divisible by $n$.

Invalid username
Login to AoPS