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Find all positive integers n for which the numbers in the set S = \{1,2, \ldots,n \} can be colored red and blue, with the following condition being satisfied: The set S \times S \times S contains exactly 2007 ordered triples \left(x, y, z\right) such that:

(i) the numbers x, y, z are of the same color,
and
(ii) the number x + y + z is divisible by n.

Author: Gerhard Wöginger, Netherlands

Slični zadaci

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