Question

Find the value of (b-a)? Given a and b are coprime to each other

Answer 1

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If a and b are two relatively prime positive integers such that ab is a square, then a and b are squares.

I need to prove this statement, so I would like someone to critique my proof. Thanks

Since ab is a square, the exponent of every prime in the prime factorization of ab must be even. Since a and b are coprime, they share no prime factors. Therefore, the exponent of every prime in the factorization of a (and b) are even, which means a and b are squares