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Thread: primitive root question

  1. November 17th 2009, 07:24 PM #1
    ezong
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    primitive root question

    How do I show that 2^{1996} \equiv 1 (mod 1997) given 1996= (2^2)(499)? There's probably an easy way but I'm just not that smart.

    I forgot to mention you have to show that 1997 is prime
    Last edited by ezong; November 17th 2009 at 07:50 PM.
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  2. November 17th 2009, 07:33 PM #2
    aman_cc
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    Quote Originally Posted by ezong View Post
    How do I show that 2^{1996} \equiv 1 (mod 1997) given 1996= (2^2)(499)? There's probably an easy way but I'm just not that smart.
    Can't you use Fermat's Little Theorem?
    Fermat's little theorem - Wikipedia, the free encyclopedia
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