MathDB
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 aa and bb such that the numbers a+1ba+\frac1b and b+1ab+\frac1a are different colors.