Let $p$ be an odd prime of the form $p=2^m+1$, for some positive integer $m$. Let $g$ be a primitive root mod $p$ with $1 \le g \le p$.

Question

Let $p$ be an odd prime of the form $p=2^m+1$, for some positive integer $m$. Let $g$ be a primitive root mod $p$ with $1 \le g \le p$. How many such $g$ are there?

Answer 1

Hint: There are $\varphi(\varphi(p))$ primitive roots of any prime $p$.