A finite field of order $p^n$ has characteristic $p$.
63659
If D is an Integral Domain and has finite characteristic p, prove p is prime.
129476
The trace map in a finite field.
19968
Describe all $p^{n}$ (in terms of congruence conditions of $p$ and $n$) for which $x^{2}+1$ irreducible over $\mathbb{F}_{p^{n}}$.
121890
Proof that $ p $ | ${ p^n \choose k } $ for any prime $p$ and $ k < p^n$
48405
Why does the characteristic of a finite field always have to be prime?
119808
Proving that $n$-cycle has order $n$
81221
The prime number theorem over a finite field - Lang's *Algebra*, Chapter V, Exercise 23(b)
139499
The algebraic closure of a finite field and its Galois group
104851
A finite field cannot be an ordered field.
128305
$PGL(n, F)=PSL(n, F)$
140106
How to prove a finite field is not ordered?
132133
Number of elements of a finite field
96549
Can we have a perfect field of characteristic $p$ with a non-archimedean valuation?
73652
Exhibiting an isomorphism between two finite fields
133878
Ring of order $p^2$ is commutative.
57884
Number of monic irreducible polynomials of prime degree $p$ over finite fields
157841
Existence of a non-abelian group of order $p^n$.