Prove $x^4 +x+1$ is irreducible in $\mathbb{Z}/2\mathbb{Z}[x]$
134726
Show the polynomial is irreducible in $\textbf Z_2$
157031
Express $x^8-x$ as a product of irreducibles in $\Bbb Z_2[x]$
16035
Irreducibility of $X^{p-1} + \cdots + X+1$
19968
Describe all $p^{n}$ (in terms of congruence conditions of $p$ and $n$) for which $x^{2}+1$ irreducible over $\mathbb{F}_{p^{n}}$.
27942
showing that $n$th cyclotomic polynomial $\Phi_n(x)$ is irreducible over $\mathbb{Q}$
53669
Prove that the polynomial $(x-1)(x-2)\cdots(x-n) + 1$, $ n\ge1 $, $ n\ne4 $ is irreducible over $\mathbb Z$
93291
Method for determining irreducibles and factorising in $\mathbb Z[\sqrt{d}]$
156356
Proof that $x^n+\frac{1}{x^n}\in \mathbb Z$ by complete induction
121479
Why is $X^4+1$ reducible over $\mathbb F_p$ with $p \geq 3,$ prime
64878
Is this polynomial irreducible in $\mathbb{Q}$?
66355
A sufficient condition for irreducibility of a polynomial in an extension field.
81377
Show that $x^n + x + 3$ is irreducible for all $n \geq 2.$
121714
Show that the polynomial $X^5 + X^3 + \bar{1}$ in $(\mathbb{Z}/2\mathbb{Z}[X])$ is irreducible
124131
Show that $(x-1)^2$ is a factor of $x^n -nx +n-1$
102422
Irreducibly of $x^5-x-1$ over $\mathbb{F}_3$
344
Prove that if $p\in \mathbb{Z}$ is irreducible, then it is also prime.
85459
$x^3+x+1$ irreducible over $\mathbb{F}_2$, $\theta$ root, compute powers of $\theta$