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Homework Help: Primitive roots

  1. Dec 7, 2004 #1
    let g be a primitive root of the odd prime p
    show that -g is a primitive root or not according as
    p==1 ( mod 4) or p==3(mod4)

    how would i start in solving this problem
    thanks
    :cool:
     
  2. jcsd
  3. Dec 7, 2004 #2
    For p==1 Mod 4, there exists an X such that X^2 ==-1 Mod p. This is not true for p==3 Mod 4. If x is a primitive root then x^((p-1)/2) = -1 since the smallest power of x that is 1 Mod p is x^(p-1). So, those are the facts needed.
     
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