Irreducibility of $x^{2^n}+x+1$ over $\mathbb{Z}_2$
74224
On irreducible factors of $x^{2^n}+x+1$ in $\mathbb Z_2[x]$
103238
Conjugates of ${\sqrt 5 + \sqrt 6 }$ over $\mathbb{Q}$ and irreducibility of $x^4 -22x^2+1$ (for minimal polynomial)
77620
Irreducible polynomials over $\mathbb Q$ and $\mathbb Z $
81377
Show that $x^n + x + 3$ is irreducible for all $n \geq 2.$
134726
Show the polynomial is irreducible in $\textbf Z_2$
53669
Prove that the polynomial $(x-1)(x-2)\cdots(x-n) + 1$, $ n\ge1 $, $ n\ne4 $ is irreducible over $\mathbb Z$
19968
Describe all $p^{n}$ (in terms of congruence conditions of $p$ and $n$) for which $x^{2}+1$ irreducible over $\mathbb{F}_{p^{n}}$.
53012
Irreducibility of a polynomial if it has no root (Capelli)
64878
Is this polynomial irreducible in $\mathbb{Q}$?
90612
Show that $9+9x+3x^3+6x^4+3x^5+x^6$ is irreducible given one of its roots
27577
An irreducible polynomial of degree coprime to the degree of an extension is irreducible over this extension
121714
Show that the polynomial $X^5 + X^3 + \bar{1}$ in $(\mathbb{Z}/2\mathbb{Z}[X])$ is irreducible
85459
$x^3+x+1$ irreducible over $\mathbb{F}_2$, $\theta$ root, compute powers of $\theta$
25471
Irreducibility of $x^n-x-1$ over $\mathbb Q$
76640
Show that the polynomial $x^3-xy^2+y+1$ is irreducible in $\mathbb{Q}[x,y]$
10821
Using Eisenstein criterion show that $x^3+x^2-2x-1$ is irreducible?
10885
Existence of irreducible polynomials over finite field