Abstract
A lattice polygon II is a simple polygon whose vertices are points of the integral lattice. We let b = b(H) denote the number of lattice points on the boundary of H, and c = c(Hl) the number of lattice points interior to II. In 1900, Pick [1] proved that the area of H is given by A((H) = 2 b + c 1. More recently it has been shown [2] that if II is convex and has at least one interior lattice point, then b 0. By suitably reflecting II we may assume that there exist parallel support lines to H n H at P, R which have non-negative slope. Hence there exist h > 0, k > 0 such that II n H is supported
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