Spanish Mathematical Olympiad 2005, Problem 2
Source: 2005 Spanish Mathematical Olympiad
July 17, 2017
algebranumber theory
Problem Statement
Is it possible to color points in the Cartesian Plane with integer coordinates with three colors, such that each color appears infinitely many times on infinitely many lines parallel to the -axis and that any three points, each of a different color, are not in a line? Justify your answer.