We know every finite field F of size q = p^n has a primitive root r (an element whose powers give all the nonzero elements of the field). Prove that r^s is another primitive root, where s has no factor in common with p^n - 1.
Okay, I'm not sure where to begin here. I guess since s and p^n - 1 don't have common factors, their gcd must be 1 = a*s + b*(p^n - 1) for some a and b, but this doesn't seem to go anywhere. We haven't technically learned anything like Euler's Totient function yet in class, so I can use that.