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Math Help - Euler phi function

  1. #1
    Junior Member Kanwar245's Avatar
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    Euler phi function

    How can I show by induction that

    \phi(p^k) = p^{k-1}(p-1) where \phi(p) = p - 1
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  2. #2
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    Re: Euler phi function

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

    Euler phi function-mhfphiofptothen.png
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  3. #3
    Junior Member Kanwar245's Avatar
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    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.
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