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Reals a,b such that a+b and ab are different colours

Source: XVIII Tuymaada Mathematical Olympiad (2011), Junior Level

July 31, 2011
combinatorics unsolvedcombinatorics

Problem Statement

Each real number greater than 11 is coloured red or blue with both colours being used. Prove that there exist real numbers aa and bb such that the numbers a+ba+b and abab are of different colours.
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