primitive roots

[b0mb0nika]

let g be a primitive root of the odd prime p
show that -g is a primitive root or not according as
p==1 ( mod 4) or p==3(mod4)

how would i start in solving this problem
thanks
:cool:

[robert Ihnot]

For p==1 Mod 4, there exists an X such that X^2 ==-1 Mod p. This is not true for p==3 Mod 4. If x is a primitive root then x^((p-1)/2) = -1 since the smallest power of x that is 1 Mod p is x^(p-1). So, those are the facts needed.