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.

Re: Indices and primitive roots

Can you check your question? (2) and (3) imply that $\displaystyle p=1$ which is totally trivial. The fact that you use the symbol *p* suggests that you want $\displaystyle p$ 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? (Thinking)

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