Problem

Source: Iran Third Round MO 1997, Exam 2, P3

Tags: analytic geometry, number theory, least common multiple, combinatorics unsolved, combinatorics



Let $d$ be a real number such that $d^2=r^2+s^2$, where $r$ and $s$ 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 $d$ have different colors.