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.