Why are there $p^n$ elements in the quotient field $\mathbb{F}_p [x]/ (f)$
58490
Polynomials, finite fields and cardinality/dimension considerations
78835
An automorphism of the field of $p$-adic numbers
121301
What are the roots of an irreducible $p\in F[X]$ in the field extension $F[X]/\langle p\rangle$?
8494
Proof Check: Number of elements of $\mathbb{F}_{p^{n}}$ of the form $a^{p}-a$ for some $a \in \mathbb{F}_{p^{n}}$.
46821
Finding roots in $\mathbb{Z}_p$
77862
Question about fields and quotients of polynomial rings
3703
Order of finite fields is $p^n$
80295
Field extensions and algebraic/transcendental elements
93328
$\mathbb{F}_p[X]/(X^2+X+1)$ is a field iff $p \equiv 2 \bmod 3$
121479
Why is $X^4+1$ reducible over $\mathbb F_p$ with $p \geq 3,$ prime
155991
Is it the case that every quotient ring ${F[x]}/{(p(x))}$ is a PID?
129597
Is a field perfect iff the primitive element theorem holds for all extensions, and what about function fields
10627
When is $X^n-a$ is irreducible over F?
141418
When is $\mathbb{F}_p[x]/(x^2-2)\simeq\mathbb{F}_p[x]/(x^2-3)$ for small primes?
50412
Prime elements in $\mathbb{Z}/n\mathbb{Z}$
156859
Proving that $GF(p^n)$ contains a unique subfield isomorphic to $GF(p^m)$ if and only if $m$ is a divisor of $n$.
145140
Subfield of $\mathbb{Q}(\sqrt[n]{a})$