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I understand that if two coprime integers a and b are such that $ab=x^2$, then a and b must also be perfect squares.

Are there any similar properties if $ab=y^3$?

Liv
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    Yes, again assuming they are relatively prime. –  Dec 06 '19 at 20:50
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    Based off the title I’m assuming that in both propositions $a$ and $b$ are coprime. If that is the case, this also applies to $ab = x^3$ and generalized to arbitrary powers. – Snacc Dec 06 '19 at 20:51
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    You can find many other related questions via the "linked" question on the linked dupes. – Bill Dubuque Dec 06 '19 at 20:56

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