question is as follows, and then I'll describe the headway I've made so far.
"Let p be an odd prime, and suppose that q=2p+1 is also prime. Prove that if a is incongruent to 1 and incongruent to -1 mod q, then (-a^2) is a primitive root modulo q."
My progress: I have shown that q must be congruent to 3 modulo 4. Further, I've proved previously that this means that there does not exist an integer x such that x^2 is congruent to -1 modulo q. So we have that (-a^2) CANNOT be congruent to 1 modulo q. From here, however, I am totally at a loss as to how to proceed.
All help appreciated. Thanks in advance.