Show that $U(17)$ is a cyclic group

Question

In this answer, here, a theorem is stated which says,

Theorem- $U(n)$ is cyclic iff $n= 2,4,p^k,2p^k$ where p is an odd prime.

For $U(17)$, it doesn't satisfy any of the $n$ conditions stated in the theorem.

What am I missing?

Answer 1

Hint: Let $$k=1.{}{}{}{}{}{}$$