Primitive roots: If $p$ is a prime such that $p\equiv 1 \pmod 4$, and $a$ is a primitive root, then $-a$ is also a primitive root.
In this particular question I did show that in fact $(-a)^{p-1} \equiv 1 \pmod 4$, what is trivial. But, how can I assure that $p-1$ is its order?
Thanks a lot.