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Partition N so that k, 2k,..., 12k are in different subsets

Source: XVII Olimpíada Matemática Rioplatense (2008)

July 24, 2011
modular arithmeticparameterizationnumber theorynumber theory unsolved

Problem Statement

Can the positive integers be partitioned into 1212 subsets such that for each positive integer kk, the numbers k,2k,…,12kk, 2k,\ldots,12k belong to different subsets?
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