Let $x$ and $y$ be positive integers and let $\gcd(x,y)=6$. How do we find all the values for $\gcd(x^2,y^3)$? How can we show that these are the only possibilities?
Possible values of $\gcd(x^2, y^3)$ when $\gcd(x,y)=6$
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elementary-number-theory