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?
3703
Order of finite fields is $p^n$
97729
Show that a polynomial $f(x)$ over a field $k$ is irreducible if and only if the polynomial $f(x+1)$ is irreducible
73652
Exhibiting an isomorphism between two finite fields
43059
Show that $g^k=e$ if and only if the order of $g$ is finite and divides $k$.
55719
Order of general- and special linear groups over finite fields.
131971
If $k>0$ is a positive integer and $p$ is any prime, when is $\mathbb Z_p[\sqrt{k}] =\{a + b\sqrt k~|~a,b \in\mathbb Z_p\}$ a field.
92672
Number of elements which are cubes/higher powers in a finite field.
50413
Proof: if $p$ is prime, and $0<k<p$ then $p$ divides $\binom pk$
118610
Are all extensions of finite fields cyclic?
62996
A problem regarding the proof of ${p^nk\choose p^n}\equiv k\mod p$, where $p\nmid k$.
78350
When does a finite ring become a finite field?
100605
let $G$ to be finite abelian group of order O(G), let n to be prime number and (O(G),n)=1 prove that $g=x^n$ for any $ x \in G$
6855
Subfields of finite fields
76813
The ring $ℤ/nℤ$ is a field if and only if $n$ is prime
62615
If F is a finite field, then $F^F=P_F$.
55429
Why does a Galois field have to have an order of $p^n$ where $p$ is prime?
131385
How to provide a counterexample for if $n$ is prime, then $2^n -1$ is prime