If p is a prime what values of $ a\leq p^{n}$ have $\text{gcd}(a, p^{n}) >1$?

48 Views Asked by At

Hi guys need your help.

Sorry but I don't understand how to use latex. So really sorry for the writing. The question is if p is prime what values of $ a\leq p^{n}$ have $\text{gcd}(a, p^{n}) >1$?

Is it correct for me to assume that a could be multiple of p from $p^0$ to $p^{n-1}$, since all of them share common factor of at least $p$. But in this case we won't include $p^0$ since the question said so.

Is it correct? If it is, how do I properly make a point about my statement?