Prove that if $\displaystyle q$ does not divide $\displaystyle p$, then $\displaystyle q^n$ does not divide $\displaystyle p^n$.
This isn't actually homework or anything, just a hypothesis I observed.
Ahhhh... But what TPH didn't tell you is that you have to be careful of the following trap:
$\displaystyle \sqrt{2}$ is not a whole number.
But $\displaystyle (\sqrt{2})^2 = 2$ is.
What you would need to show is something like that $\displaystyle \sqrt{2}$ cannot be expressed as a rational number $\displaystyle \frac{p}{q}$.
-Dan