Pentagon in the plane [lattice point in a pentagram]
Source: Russia 2000
May 16, 2004
analytic geometrygeometryparallelogramgeometry unsolved
Problem Statement
We are given a convex pentagon in the coordinate plane such that , , , , are lattice points. Let denote the convex pentagon bounded by the five diagonals of the pentagon (so that the vertices of are the interior points of intersection of diagonals of the pentagon ). Prove that there exists a lattice point inside of or on the boundary of .