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I would like if someone could provide or show me where I can find the proof that $\mathbb{Z} _n^*$ is cyclic when n is prime. In particular I'm after a simple proof that involves fermats little theorem. Would appreciate it best regards.

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  • $\begingroup$ Not a duplicate as I'm looking for a specific and less general result. In particular trying to avoid theory I do not know. $\endgroup$ – Dead_Ling0 Jun 21 '19 at 16:05
  • $\begingroup$ Well, at some point you'll need to use the fact that, $\pmod p$, a non-zero polynomial of degree $d$ can have no more than $d$ roots. That follows instantly from the fact that the integers, $\pmod p$ form a field. I don't think you'll find a short cut round that fact. $\endgroup$ – lulu Jun 21 '19 at 16:12
  • $\begingroup$ @lulu "instantly" is a bit of a stretch (at this level), but it does follow easily by inductively applying the Factor Theoem e.g. here, or by using $\,x-a\,$ is prime over a domain. $\ \ $ $\endgroup$ – Bill Dubuque Jun 21 '19 at 16:33