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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 n>1n>1 with the following property: For each colouring of the lattice points in the plane with nn colours, there are three lattice points of the same colour forming an isosceles right triangle with legs parallel to the coordinate axes.