IMO 2016 Shortlist N7

Let n be an odd positive integer. In the Cartesian plane, a cyclic polygon P with area S is chosen. All its vertices hav...

IMO 2016 Shortlist N7

Category: Number Theory

Problem

Let n be an odd positive integer. In the Cartesian plane, a cyclic polygon P with area S is chosen. All its vertices have integral coordinates, and all squares of its side lengths are divisible by n. Prove that 2S is an integer divisible by n.