Four lattice points in triangle must be collinear
Source: BAMO 2023/5
March 3, 2023
BAMOcombinatorics
Problem Statement
A lattice point in the plane is a point with integer coordinates. Let be a triangle in the plane whose vertice are lattice points, but with no other lattice points on its sides. Furthermore, suppose contains exactly four lattice points in its interior. Prove that these four points lie on a straight line.