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Number Theory Problems

  1. Jun 4, 2009 #1
    1. The problem statement, all variables and given/known data
    a > 1, k > 0. Show that k divides \phi(a^k - 1), where \phi is Euler's totient function (Hint: use some group theory).


    2. Relevant equations
    If n = p_1^{a_1}p_2^{a_2}...p_m^{a_m}, then \phi(n) = n(1 - 1/p_1)(1 - 1/p_2)...(1 - 1/p_m)


    3. The attempt at a solution
    I guess that I need somehow use the fact that \phi(n) is an order of multiplicative group U(Z/nZ), but I don't see how.

    Any suggestions are appreciated!
    Thanks!
     
  2. jcsd
  3. Jun 6, 2009 #2
    Guys, does anyone have any ideas how to do it?
     
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