# Reduced multiplicative residue modulo p [duplicate]

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.

• Not a duplicate as I'm looking for a specific and less general result. In particular trying to avoid theory I do not know. – Dead_Ling0 Jun 21 '19 at 16:05
• 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. – lulu Jun 21 '19 at 16:12
• @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. $\ \$ – Bill Dubuque Jun 21 '19 at 16:33