# Math Help - Primitive Root Question

1. ## Primitive Root Question

Show that if p is a prime and p=2q+1, where q is an odd prime and a is a positive integer with 1 < a < p-1, then p- $a^2$is a primitive root modulo p.

2. Note that $p \equiv 3 (\bmod. 4)$ what does this tell you about $-1$ ? and about $p-a^2$ ?

Next, prove that all non-quadratic residues module p (except for -1) must be primitive roots module $p$.
Hint : Count