MathDB

Each vertex of a convex polygon has integer coordinates, and no side of this polygon is horizontal or vertical. Prove that the sum of the lengths of the segments of lines of the form

x = m

m

an integer, that lie within the polygon is equal to the sum of the lengths of the segments of lines of the form

y = n

n

an integer, that lie within the polygon.
(G Galperin)

Problem Statement