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^{x}cyclic?

We haven't discussed the theorem in class that any units group of Z modulo n is iff n = 1, 2, 4, p

^{k}and 2p

^{k}(where p is an odd prime). But thanks to Deveno I know about it. So in this case, p =17 works, so the group is cyclic?

but is there a different way to show it besides using

**brute force**.