I'm a complete beginner and not sure where to go with this proof of Euclid's lemma. Any help would be greatly appreciated.
If $m$ is a positive integer and a prime number $p$ is a factor of $m^2,$ then $p$ is a factor of $m.$
So far I have:
Since we know that $m$ is a positive integer, then $m^2$ must also be positive. We also know that $p$ is positive integer, since it is a prime number.
So $m^2 = p*k$ where $k$ is positive since both $m^2$ and $p$ are positive. Therefore, $k$ is greater than or equal to $1.$