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Prove that a positive integer n, n > 1, is a perfect square if and only...

Prove that a positive integer n, n > 1, is a perfect square if and only if when we write

n = P1e1P2e2... Prer

with each Pi prime and p1 < ... < pr, every exponent ei is even. (Hint: use the Fundamental Theorem of Arithmetic!)

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