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If a prime $p$ divides $n^2$ then it also divides $n$ - Is this proof correct?
I'm learning Real Analysis by myself and I wanted to prove that if a prime $p$ divides $n^2$ where $n$ is an integer, then $p$ divides $n$ itself. I saw that proving this is the same as saying that ...
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Proof verification: Let $gcd(x,y)=1$. If $xy$ is a perfect square, then $x$ and $y$ are perfect squares.
Can someone please verify whether my proof is logically correct? :)
Let $gcd(x,y)=1$. If $xy$ is a perfect square, then $x$ and $y$ are perfect squares.
Proof:
If $xy$ is a perfect square, let $...
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