Let $p$ a prime number. Show that the polynomial $X^p-X-1 \in F_{p}[X]$ is irreducible
1487
How do I prove that $x^p-x+a$ is irreducible in a field with $p$ elements when $a\neq 0$?
121658
$x^2+y^2-1$ irreducible in $\mathbb{Q}[x,y]$?
41693
Use irreducible fibers to show $X$ is irreducible
51952
Show that $x^{n-1}+\cdots +x+1$ is irreducible over $\mathbb Z$ if and only if $n$ is a prime.
10266
Minimal polynomial reducible modulo every prime $p$
46292
Find all primes $p>2$ for which $x^2+x+1$ is irreducible in $\mathbb{F}_p[x]$
79564
Algorithm to find the irreducible polynomial
54192
Why $x^{p^n}-x+1$ is irreducible in ${\mathbb{F}_p}$ only when $n=1$ or $n=p=2$
73344
Definition of irreducible polynomial via the units of an integral domain.
70523
Proving that $x^4 - 10x^2 + 1$ is not irreducible over $\mathbb{Z}_p$ for any prime $p$.
64878
Is this polynomial irreducible in $\mathbb{Q}$?
120940
An irreducible polynomial in a subfield of $\mathbb{C}$ has no multiple roots in $\mathbb{C}$
85459
$x^3+x+1$ irreducible over $\mathbb{F}_2$, $\theta$ root, compute powers of $\theta$
91356
Irreducibility of an infinite sequence of polynomials
16035
Irreducibility of $X^{p-1} + \cdots + X+1$
146887
Prove that $f=x^4-4x^2+16\in\mathbb{Q}$ is irreducible
8977
Showing $x^{5}-ax-1\in\mathbb{Z}[x]$ is irreducible