Lattice Polygons
Source: Romanian Masters in Mathematics 2020, Problem 5
March 1, 2020
analytic geometrycombinatoricsRMMRMM 2020
Problem Statement
A lattice point in the Cartesian plane is a point whose coordinates are both integers. A lattice polygon is a polygon all of whose vertices are lattice points. Let be a convex lattice polygon. Prove that is contained in a convex lattice polygon such that the vertices of all lie on the boundary of , and exactly one vertex of is not a vertex of .