# Math Help - Euler phi function

1. ## Euler phi function

How can I show by induction that

$\phi(p^k) = p^{k-1}(p-1)$ where $\phi(p) = p - 1$

2. ## Re: Euler phi function

This is not an inductive proof, but it is very simple:

3. ## Re: Euler phi function

I'm actually trying to come up with an inductive proof; I know how to think about this in terms of counting which makes sense. However, in terms of induction I don't know how to show it.