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Determine the maximum number of elements in M

Source: IMO Shortlist 1994, N1

August 10, 2008
number theoryExtremal combinatoricsPerfect SquaresSubsetIMO Shortlist

Problem Statement

M M is a subset of {1,2,3,…,15} \{1, 2, 3, \ldots, 15\} such that the product of any three distinct elements of M M is not a square. Determine the maximum number of elements in M. M.
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