Tricky GCD problem Say we have two integers, $x$ and $y$. If $\gcd(x,y)=5$, how can we find every value for $\gcd(x^2,y)$? If you can find a list of every value, can you prove that this list is complete?

Here is something to consider: Can $\gcd(x^2,y)$ be divisible by any primes other than 5? (Note that if $p$ is any prime number, then $p$ divides $x^2$ if and only if $p$ divides $x$.)
Do you think $5^{100000}$ is a possible value for $\gcd(x^2,y)$? Why or why not? If you try to make your intuition precise about this, that should take you the rest of the way.
