Two-coloring (1,infty) implies a+1/b & b+1/a are different
Source: XVIII Tuymaada Mathematical Olympiad (2011), Senior Level
July 29, 2011
combinatorics unsolvedcombinatorics
Problem Statement
Each real number greater than 1 is colored red or blue with both colors being used. Prove that there exist real numbers and such that the numbers and are different colors.