How can I show by induction that $\displaystyle \phi(p^k) = p^{k-1}(p-1)$ where $\displaystyle \phi(p) = p - 1$
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This is not an inductive proof, but it is very simple:
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.
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