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According to Wikipedia, a cyclic number (in group theory) is one which is coprime to its Euler phi function and is the necessary and sufficient condition for any group of that order to be cyclic. Why is that true?

I can see that if $n$ is prime, that guarantees any group of order $n$ is cyclic, but I don't seem to see how to extend it to $(n,\phi(n))=1$

It would be nice if someone could explain it to me. Thanks.

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    See also [this question for more references](http://math.stackexchange.com/a/67469/742)2012-02-05

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