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Math Help - primitive root euler function

  1. #1
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    Mar 2013
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    israel
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    primitive root and euler function

    (My English is not very well but I will try to explain myself as good as I can..)

    I have 3 questions:

    1. Assume 10 is a primitive root of p, a prime number , p!=7.
    I need to prove that infinite number of this series :

    31 331 3331 ...

    is divided by p.

    2.Prove that there is no natural number n such that n=2006* fi(n)
    (when fi is euler function)

    3. This is true that if a is primitive root af n, also is opposite? why?

    Thanks!
    Last edited by userit8; March 22nd 2013 at 02:19 AM.
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