Coloring the points with rational coordinates
Source: Iran Third Round MO 1997, Exam 2, P3
June 30, 2012
analytic geometrynumber theoryleast common multiplecombinatorics unsolvedcombinatorics
Problem Statement
Let be a real number such that , where and are rational numbers. Prove that we can color all points of the plane with rational coordinates with two different colors such that the points with distance have different colors.