Question 3
Let $P=A_1A_2\dots A_k$ be a convex polygon in the plane. The vertices $A_1$, $A_2$, …, $A_k$ 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 $n$.