Pick's theorem and sums of lattice points

Karl Levy, Melvyn B. Nathanson

Published 2015-11-09Version 1

Pick's theorem is used to prove that if $P$ is a lattice polygon (that is, the convex hull of a finite set of lattice points in the plane), then every lattice point in the $h$-fold sumset $hP$ is the sum of $h$ lattice points in $P$.