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Math Help - Euler's Totient Function

  1. #1
    Member Maccaman's Avatar
    Joined
    Sep 2008
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    Euler's Totient Function

    Hi, I was just wondering if someone could confirm that the following is correct? Just a yes or no would suffice.

     \varphi (190) = 72

    Thanks
    Last edited by Maccaman; March 28th 2009 at 08:01 PM. Reason: silly question
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  2. #2
    Newbie
    Joined
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    Loma Linda, CA
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    Yes it looks correct, since

     \varphi(p^k)=(p-1)p^{k-1} for a prime p and using the fact that phi is multiplicative i.e
     \varphi(ab)= \varphi(a) * \varphi(b)

    Then

    <br />
\varphi (190) = 72<br />

    <br /> <br />
\varphi(190)=\varphi(2*19*5)=\varphi(2) * \varphi(5) * \varphi(19)<br />

    <br />
=1(2^{1-1}) *4(5^{1-1}) *18(19^{1-1}) \ { }= (2^0)*4(5^0)*18(19^0) = 4*18=72 <br />

    Yes your answer is correct. Hope this helps!
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