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Euler function-totient

  1. Nov 5, 2008 #1
    Hello, can anyone help with this question? Thank you.


    Let n even perfect number and q prime. Show that n/Φ(n)=2q/q-1.

    Φ(n) is the Euler function-totient (the number of positive integers less than or equal to n that are coprime to n)


    I have tried euler-euclid theorem but could not get it.
     
  2. jcsd
  3. Nov 5, 2008 #2

    Office_Shredder

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    Re: urgent help

    2q/(q-1) is different for different primes q, so you must have some additional condition on what q is (unless you really meant without the parentheses, in which case 2q/q-1 = 1 which makes no sense). Unless you're trying to show such a q exists?
     
  4. Nov 6, 2008 #3
    Re: urgent help

    phi(n)=phi[2^(k-1)q] where q=(2^k)-1

    phi(n)=phi(2^(k-1))phi(q)=phi(2^(k-1))(q-1)

    Is there any property I can use to finish this?
     
  5. Nov 6, 2008 #4

    Dick

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    Re: urgent help

    What's phi(2^(k-1))? There's a formula for phi for powers of a prime. (It's also the number of odd integers less than 2^(k-1)).
     
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