Prove that $x^{p^{n}}-x-a$ is reducible over GF(p).
54192
Why $x^{p^n}-x+1$ is irreducible in ${\mathbb{F}_p}$ only when $n=1$ or $n=p=2$
105910
How to prove that $[G:xHx^{-1}] = [G:H]$ given $H \le G$?
27577
An irreducible polynomial of degree coprime to the degree of an extension is irreducible over this extension
150042
Prove $x^{-1}Hx$ is a subgroup of $G$
5069
$GL_n(\mathbb F_q)$ has an element of order $q^n-1$
74777
Solvability and reducibility of a polynomial in a "chain" of finite fields
138069
Proof that $\bigcap_{a\in A} \bigg(\, \bigcup_{b\in B} F_{a,b} \, \bigg) = \bigcup_{f\in ^AB} \bigg(\, \bigcap_{a \in A} F_{a,f(a)}\,\bigg) $
10266
Minimal polynomial reducible modulo every prime $p$
66355
A sufficient condition for irreducibility of a polynomial in an extension field.
110662
Show that $P(\mathbb{N})$ is equivalent to $2^\mathbb{N}$
88181
Splitting field of $X^n-a$
3703
Order of finite fields is $p^n$
102234
Show $a^p \equiv a \mod 2p$
121890
Proof that $ p $ | ${ p^n \choose k } $ for any prime $p$ and $ k < p^n$
19968
Describe all $p^{n}$ (in terms of congruence conditions of $p$ and $n$) for which $x^{2}+1$ irreducible over $\mathbb{F}_{p^{n}}$.
4000
If every polynomial of degree 2 is reducible then $K$ is algebraically closed?
83036
f(g(x)) has a degree divisible by n