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Math Help - Primitive Roots

  1. #1
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    Primitive Roots

    I have this problem here, and I can't seem to figure out how to do it.

    "Suppose that a (mod p) is a primitive root modulo an odd prime p. If p=3(mod4) is prime, then show that -a(mod p) is never a primitive root modulo p."


    Is the proper way to go about this by somehow using the legendre symbol? Or Eulers Criterion? I'm pretty confused.

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  3. #3
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    I am sorry. Let me explain better. But that link provides an excellent hint to this problem.

    I am really not careful in the second to last line it should be a^{(p-1)/2} = -1 (mod p) instead.
    Attached Thumbnails Attached Thumbnails Primitive Roots-picture18.gif  
    Last edited by ThePerfectHacker; May 2nd 2007 at 03:52 AM.
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