For which $n$ is the group $U_n$ (group of all positive integers less than $n$ that are coprime to $n$) a cyclic group?
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$n=2,4,p^k,2p^k$($p$ is an odd prime number) – user91500 Dec 27 '13 at 12:42
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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.
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