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The set can be partitioned into 27 sets

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August 29, 2010
combinatorics proposedcombinatorics

Problem Statement

Prove that the set {1,2,...,1986}\{1, 2, . . . , 1986\} can be partitioned into 2727 disjoint sets so that no one of these sets contains an arithmetic triple (i.e., three distinct numbers in an arithmetic progression).
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