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Math Help - True or false

  1. #1
    Super Member Showcase_22's Avatar
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    True or false

    Is this statement true or false: "If \phi denotes the Euler-Phi function, there is a unique value of the number n for which \phi(n)=12".

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    \phi(13)=12. How can I prove (or disprove) that there isn't another?
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  2. #2
    Senior Member TheAbstractionist's Avatar
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    Well, 12=(3-1)(7-1) so \varphi(21)=12.
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  3. #3
    Super Member Showcase_22's Avatar
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    What did you do there?

    Also, looking on wiki, there's another: \phi(28)=12
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  4. #4
    Moo
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    Quote Originally Posted by Showcase_22 View Post


    What did you do there?
    We know that if p and q are prime numbers, then \varphi(pq)=(p-1)(q-1)

    Then, playing with the factors of 12 will bring you to the solution he found.
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  5. #5
    Super Member Gamma's Avatar
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    \phi(13)=13-1=12
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