Prove that $7$ is a primitive root modulo $p=2^s+1$.

Question

I need help with the following question:

If $1<s\in \mathbb N$ and $p=2^s+1$ is prime, so $7$ is a primitive root modulo $p$.

My thoughts: First I know: $\phi(p)=p-1=2^s$. So if $r$ is the order of $7$ modulo $p$ then $r | \phi (p)=2^s$ then $rc=2^s$ and I don't know how to continue.

Thank in advance.