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Homework Help: Primitive Roots

  1. Dec 20, 2016 #1
    Hello friends from afar.

    I ran into what I felt to be somewhat of an odd question:

    Prove that some odd numbers are primitive roots modulo pm for each odd prime p and each positive integer m.

    It feels dodgy given that any odd number n = p1p2 ⋅⋅⋅ ps cannot be a primitive root of a prime number involved in its prime factorization. I just needed to be sure. Many thanks.
  2. jcsd
  3. Dec 20, 2016 #2


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    2017 Award

    Staff: Mentor

    The wording is quite disturbing and I stumbled upon the same argument as you. "some odd numbers" looks strange.
    It would make more sense the other way around (or I didn't get the point either):

    For each odd prime ##p## and each positive integer ##m## prove that some odd numbers are primitive roots modulo ##p^m.##
  4. Dec 20, 2016 #3
    Indeed. I'm guessing yours is how it's done, since it seems like the original could be semantically interpreted like that. Thanks.
  5. Dec 20, 2016 #4


    Staff: Mentor

    In future posts, please don't delete the homework template...
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