Primitive roots of $2^{16} + 1$

Question

I have a primitive root $ \alpha $ of a number $ p = 2^{16} + 1$.
How can I show if $ \alpha^{3} $ and $\alpha^{14}$ are primitive roots as well?

Answer 1

Hint: Use the Gauss Theorem: If $a$ is a primitive root then all primitive roots have the form $a^s$, $(s,p-1)=1,$ $p$ - prime number.