For which $n$ is the group $U_n$ (group of all positive integers less than $n$ that are coprime to $n$) a cyclic group?
2026-04-03 09:11:35.1775207495
A question concerning cyclic property of a group
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$U_n$ is cyclic if and only if there is a primitive root mod $n$. We know that the positive integers $n$ for which there are primitive roots are $n = 2, \,4, \,p^k, \text { and }\,2p^k,\;$ where $p$ is an odd prime.