I have this question on a homework sheet:
Claim:$\Phi_{p}(x)=1+x+x^2+...+x^{p-1}\space$ for $p$ prime.
which was followed by the claim that $\Phi_{p^n}(x)=\Phi_p(x^{p^{n-1}})$ which I have done via the Möbius function definition. The unsolved claim is supposed to be easier (that's how our sheets are structured) and presumably related, but I don't know how to go about it. Please help!