An isosceles right triangle in a colouring of lattice points
Source: Bundeswettbewerb Mathematik 2018, Round 2, Problem 4
February 5, 2019
combinatoricscombinatorics unsolvedcombinatorial geometry
Problem Statement
Determine alle positive integers with the following property:
For each colouring of the lattice points in the plane with colours, there are three lattice points of the same colour forming an isosceles right triangle with legs parallel to the coordinate axes.