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I want to prove the following theorem

Let $G$ be a finite group such that $(|G|,\phi(|G|))=1$ (where $\phi$ is the totient function), then $G$ is cyclic.

I used this theorem so far, but suddenly I want to prove this theorem, what can be the nice approach for proving this theorem?

phy_math
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  • See https://math.stackexchange.com/questions/106085/order-of-cyclic-groups-and-the-euler-phi-function – lhf Feb 25 '21 at 10:26

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