hello, I want to ask the same comment @mmm made here (which was no longer responded to by the author of the answer)
https://math.stackexchange.com/questions/748792/r-primitive-root-of-prime-p-where-p-equiv-1-mod-4-prove-r-is-also-a
Why is it that just because a power of -r is congruent to r then -r must be a primitive root?