only one lattice point in triangle with lattice vertices
Source: 1955 Hungary - Kürschák Competition p3
October 10, 2022
geometryanalytic geometrylatticeCentroid
Problem Statement
The vertices of a triangle are lattice points (they have integer coordinates). There are no other lattice points on the boundary of the triangle, but there is exactly one lattice point inside the triangle. Show that it must be the centroid.