I think I've found a proof for the following but would really appreciate if someone could either point out where I've gone wrong (there are a couple of steps which I'm not 100% happy with) or perhaps suggest a more simple approach. Anyway, here is the problem:

Let p be prime. Let p == 2 mod 3 and p-1 = 4q (for some prime q)>

1) a) Prove

My proof:

which contradictions our assumption that

Could anyone tell me if this proof is correct? Thanks!