MathDB
Numbers in set can be colored red and blue

Source: IMO Shortlist 2007, C3, AIMO 2008, TST 2, P2

July 13, 2008
combinatoricsmodular arithmeticcountingIMO Shortlisttriplets

Problem Statement

Find all positive integers n n for which the numbers in the set S \equal{} \{1,2, \ldots,n \} can be colored red and blue, with the following condition being satisfied: The set S×S×S S \times S \times S contains exactly 2007 2007 ordered triples (x,y,z) \left(x, y, z\right) such that: (i) the numbers x x, y y, z z are of the same color, and (ii) the number x \plus{} y \plus{} z is divisible by n n. Author: Gerhard Wöginger, Netherlands
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