$x^8-1$ - Irreductible polynomials over $\mathbb{Z}/3\mathbb{Z}$.
37068
How could it possible to factorise $x^8-1$ in product of irreducibles in the rings $(\mathbb{Z}/2\mathbb{Z})[x]$ and $(\mathbb{Z}/3\mathbb{Z})[x]$?
91356
Irreducibility of an infinite sequence of polynomials
53669
Prove that the polynomial $(x-1)(x-2)\cdots(x-n) + 1$, $ n\ge1 $, $ n\ne4 $ is irreducible over $\mathbb Z$
154360
Show $f$ can't be irreducible over a finite field if $f^\prime$ is the zero polynomial.
63605
Irreducible polynomials and affine variety
154373
How many irreducible monic quadratic polynomials are there in $\mathbb{F}_p[X]$?
108385
Irreducible factors of $x^8 - x$ in $Z/2Z[x]$
31074
Mathematical Induction divisibility $8\mid 3^{2n}-1$
38364
Showing that $x^n -2$ is irreducible in $\mathbb{Q}[X]$
19968
Describe all $p^{n}$ (in terms of congruence conditions of $p$ and $n$) for which $x^{2}+1$ irreducible over $\mathbb{F}_{p^{n}}$.
10627
When is $X^n-a$ is irreducible over F?
81377
Show that $x^n + x + 3$ is irreducible for all $n \geq 2.$
103552
The minimal polynomial of a primitive $p^{m}$-th root of unity over $\mathbb{Q}_p$
66355
A sufficient condition for irreducibility of a polynomial in an extension field.
132665
Show $p(X)$ (over a field) is irreducible iff $p(X+a)$ is irreducible
64878
Is this polynomial irreducible in $\mathbb{Q}$?
8977
Showing $x^{5}-ax-1\in\mathbb{Z}[x]$ is irreducible