There is a finite field of order $n$ if and only if $n=p^k$ for a prime p and an integer k - where do I get a proof of it?

Asked Apr 26 '17 at 15:46

Active Apr 26 '17 at 15:46

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this is a quite easy theorem which shouldn't be too hard to prove - I need it for some presentation; However I'm looking for the proof in the internet and can't find it - does anyone know where I can find the formal proof of it?

asked Apr 26 '17 at 15:46

Here: https://math.stackexchange.com/questions/72856/order-of-finite-fields-is-pn – J126 Apr 26 '17 at 15:48
If $\mathbb{F}_q$ is a finite field of characteristic $p$, then $p$ must be prime and $q = p^n$ for some $n$ (characteristic $p$ means that the subfield generated by $1$ is $\mathbb{Z}/p\mathbb{Z}$) – reuns Apr 26 '17 at 21:37

There is a finite field of order $n$ if and only if $n=p^k$ for a prime p and an integer k - where do I get a proof of it?

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