Thread: Primitive Roots

I have this problem here, and I can't seem to figure out how to do it.

"Suppose that a (mod p) is a primitive root modulo an odd prime p. If p=3(mod4) is prime, then show that -a(mod p) is never a primitive root modulo p."


Is the proper way to go about this by somehow using the legendre symbol? Or Eulers Criterion? I'm pretty confused.

I think you mean this.

I am sorry. Let me explain better. But that link provides an excellent hint to this problem.

I am really not careful in the second to last line it should be a^{(p-1)/2} = -1 (mod p) instead.