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Dirichlet's Theorem on Arithmetic Progressions

  1. Aug 2, 2011 #1

    I'm wondering if this is true, or if anyone has seen this before:

    Let q, t be coprime integers. Then there exist infinitely many primes r such that
    1. q is primitive root modulo r and
    2. r = q + kt, for some k > 0.

    If we take away 1, this becomes Dirichlet's Thm.


    But could this be true when we allow 1 ?
    Last edited: Aug 2, 2011
  2. jcsd
  3. Aug 3, 2011 #2
    The problem is definitely tougher than Dirichlet's Thm .!
  4. Aug 4, 2011 #3
    Haha, was just wondering if this had been done. It's definitely not in my analytic number theory book!
    Last edited: Aug 4, 2011
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