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Azerbaijan BMO TST
2024 Azerbaijan BMO TST
2024 Azerbaijan BMO TST
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Azerbaijan BMO TST
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Product of pairs is a perfect square
Let
n
n
n
be a positive integer. Using the integers from
1
1
1
to
4
n
4n
4
n
inclusive, pairs are to be formed such that the product of the numbers in each pair is a perfect square. Each number can be part of at most one pair, and the two numbers in each pair must be different. Determine, for each
n
n
n
, the maximum number of pairs that can be formed.