For what possible values of n is U(n) cyclic?Is there any general result regarding this?If yes please could anyone state it and possibly give me a hint about its proof.
2026-04-05 00:53:52.1775350432
The cyclic nature of group U(n)
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The group is cyclic if and only if $n=1,2,4,p^k$ or $2p^k$ where $p$ is an odd prime.
Gauss knew this. It seems to me the result is fairly nontrivial, requiring the proof that there is a primitive element mod $n$ in those, and only those, cases. If memory serves this problem was at least partially considered in his Disquisitiones Arithmeticae of $1801$.