Show all primitive roots can be obtained from this fixed primitive root.

Question

Let $g$ be a primitive root modulo $p$. Show that all the primitive roots can be obtained from this fixed primitive root as $g^k$ where $1 ≤ k < p$ and $gcd(k, p − 1) = 1$.

Stuck on this problem.

Answer 1

Every nonzero element mod $p$ can be expressed in terms of the primitive root in that way, hence in particular so can the other primitive roots be.

Answer 2

Hint : Use fermat's little theorem.