Let p be a prime, m an odd positive integer such that $ p^e||m$, where $ e>1 $ is an integer. I am trying to show that
$$ \phi(p^e)=p^e-p^{e-1}\nmid p^et-1=m-1 $$
Is it enough to just say that the left-hand side will be some multiple of p whereas the right hand side will be some multiple of p minus one so the right-hand side cannot divide the left?