Israel 2013 Q5 - Triangle in the integer lattice
Source: Israel National Olympiad 2013 Q5
August 8, 2019
combinatoricsgeometrynumber theorylattice points
Problem Statement
A point in the plane is called integral if both its and coordinates are integers. We are given a triangle whose vertices are integral. Its sides do not contain any other integral points. Inside the triangle, there are exactly 4 integral points. Must those 4 points lie on one line?