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...
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.