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Number theory proof.

  1. Oct 10, 2011 #1
    hey guys been staring at this question for a few days and frustratingly nothing springs to mind. If any1 could offer some direction that would be awsome :)

    let n be a positive integer, and let p be a prime. Show that if e is a positive integer and p^e|n then p-1|∅(n) and p^(e-1)|∅(n)
     
  2. jcsd
  3. Oct 11, 2011 #2

    mathwonk

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    explain your notation and you will likely get more answers.
     
  4. Oct 12, 2011 #3

    Deveno

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    my guess is he(?) intends to indicate the totient function.
     
  5. Mar 11, 2012 #4
    I'm assuming you're using ∅ to indicate Euler's Totient Function/the Euler Phi-Function.

    The definition of the totient function/Euler Phi-Function I learned for a natural number n with prime factorization p1^a1 *p2^a2***pn^an, where some of the exponents may be 0 is:

    (p1-1)*p1^(a1-1)*(p2-1)*p2^(a2-1)***(pn-1)*pn^(an-1).

    So if you know that p^e divides n, the rest should follow from the definition of the Euler Phi-Function.
     
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