# A quick one

by bobsmiters
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 Sci Advisor HW Helper P: 2,586 $$\mathbb{Z} = \{ 0,\, 1,\, \dots ,\, 40,\, 41\, \dots \}\ \mathbf{\cup \ \{-1,\, -2,\, \dots \}}$$ Start with the assumption that a and b are coprime integers whose product is square. What can you deduce about the prime factors of a and b? You should be able to deduce something almost like that a and b should both be square, but the fact that you're looking for integers will provide a loophole.
 Quote by AKG $$\mathbb{Z} = \{ 0,\, 1,\, \dots ,\, 40,\, 41\, \dots \}\ \mathbf{\cup \ \{-1,\, -2,\, \dots \}}$$ Start with the assumption that a and b are coprime integers whose product is square. What can you deduce about the prime factors of a and b? You should be able to deduce something almost like that a and b should both be square, but the fact that you're looking for integers will provide a loophole.