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product of 2 different elements in same subset is never a perfect square

Source: Canada Repêchage 2019/4 CMOQR

March 1, 2020
partitionnumber theorySubsetsPerfect Square

Problem Statement

Let nn be a positive integer. For a positive integer mm, we partition the set {1,2,3,...,m}\{1, 2, 3,...,m\} into nn subsets, so that the product of two different elements in the same subset is never a perfect square. In terms of nn, fi nd the largest positive integer mm for which such a partition exists.
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