Find polychromatic isosceles triangle in 3-colored n-gon!
Source: 2016 IMO Shortlist C3
July 19, 2017
combinatoricsIMO ShortlistColoringRamsey Theory
Problem Statement
Let be a positive integer relatively prime to . We paint the vertices of a regular -gon with three colours so that there is an odd number of vertices of each colour. Show that there exists an isosceles triangle whose three vertices are of different colours.