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Thread: Phi Function Proof

  1. #1
    May 2009

    Phi Function Proof

    Show that there are infinitely many integers n for which \phi(n) is a perfect square. Hint: Consider  n = 2^{2k + 1}

    I'm trying a proof by induction but I get stuck when considering the k + 1th term.
    Thanks in advance!
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  2. #2
    Senior Member
    Apr 2009
    Atlanta, GA

    Phi Function Properties

    When p is prime, \phi(p^a)=p^a(1-\frac{1}{p}). Therefore, \phi(2^{2k+1})=p^{2k+1}(1-\frac{1}{2})=p^{2k}=(p^k)^2

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