10.2

Part of 2002 All-Russian Olympiad Regional Round

Problems(1)

convex polygon that contains >=m^2+1 lattice pointa has m+1 collinear lattice

Source: All-Russian MO 2002 Regional (R4) 10.2

A convex polygon on a plane contains at least

m^2+1

points with integer coordinates. Prove that it contains

m+1

points with integer coordinates that lie on the same line.

combinatoricscombinatorial geometrylattice pointsconvex polygon