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Math Help - Reload this Page Euler's Totient Function Proving

  1. #1
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    Reload this Page Euler's Totient Function Proving


    I need some help on how to prove this statement. I don't know where to start!

    Prove that if d and n are positive integers such that d|n, then φ(dn) = dφ(n).


    A lot of help is appreciated.. I tried writing

    and where through are the same for both and .


    But I don't know where to go from there....


    Thanks
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  2. #2
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    Quote Originally Posted by kapowiee View Post

    I need some help on how to prove this statement. I don't know where to start!

    Prove that if d and n are positive integers such that d|n, then φ(dn) = dφ(n).


    A lot of help is appreciated.. I tried writing

    and where through are the same for both and .


    But I don't know where to go from there....


    Thanks

    Perhaps recalling that n=p^{a_1}_1\cdot \ldots \cdot p^{a_r}_r \Longrightarrow  \phi(n)=n\prod\limits_{k=1}^r\left(1-\frac{1}{p_k}\right) could help a lot...

    Tonio
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