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Homework Help: Solving a congruence

  1. Feb 12, 2008 #1
    1. The problem statement, all variables and given/known data
    Find all primes p (as a congruence) such that 11^((p-1)/2) = 1 modp

    3. The attempt at a solution
    I'm new to congruences and I don't really know to approach this. Any help greatly appreciated!
  2. jcsd
  3. Feb 12, 2008 #2


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    That looks like a candidate for Fermat's Little Theorem: ap-1 is congruent to 1 for any prime p and any a not a multple of p. For what prime p is (p-1)/2 also a prime?
  4. Feb 12, 2008 #3
    Thanks for the reply. I did a few computations and indeed it seems to only hold for when (p-1)/2 is also a prime. I still don't see how Little Fermat implies this though...
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