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Math Help - Indices and Primitive Roots

  1. #1
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    Indices and Primitive Roots

    This is really stumping me:

    1. If a and b satisfy the relation ab = = 1 (mod p).

    2.If a and b satisfy the relation a + b = = 0 (modp)

    3. If a and b satisfy the relation a+b = = 1(mod p)

    ...Show how the indices of a and b are related.

    In the first question, it seems I(a)+I(b)= 0 mod p-1. This I can prove relatively easily.
    In the second, I have noticed that I(a)+I(b) is always even. Why does this happen? Can I prove it?
    I've got nothing on the third one.
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  2. #2
    Member Sylvia104's Avatar
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    Re: Indices and primitive roots

    Can you check your question? (2) and (3) imply that p=1 which is totally trivial. The fact that you use the symbol p suggests that you want p to be prime, but no prime number can satisfy all the conditions you stated simultaneously. Can you check that you've copied the question correctly?
    Last edited by Sylvia104; April 3rd 2012 at 02:19 AM.
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  3. #3
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    Re: Indices and Primitive Roots

    I should have been more clear. I am trying to infer something about each case individually. 1,2,3 are separate problems. p is prime also
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