Let $k$ be a field of characteristic $\neq 2$. Then $x^6-xy+y^6$ is irreducible in $k[x,y]$.
70249
Irreducibility of Polynomials in $k[x,y]$
48093
Irreducible polynomial in field extension
85459
$x^3+x+1$ irreducible over $\mathbb{F}_2$, $\theta$ root, compute powers of $\theta$
134726
Show the polynomial is irreducible in $\textbf Z_2$
76017
Prove that $x^3-2$ and $x^3-3$ are irreducible over $\Bbb{Q}(i)$
32391
Show that $x^2+x+4$ is irreducible over $\mathbb Z_{11}$.
133312
Are these polynomials irreducible in $\mathbb{Q}[x]$?
8977
Showing $x^{5}-ax-1\in\mathbb{Z}[x]$ is irreducible
96087
Let $\mathbb{F}_2 \cong \mathbb{Z}/2\mathbb{Z}$. Is $x^4+x^2+1$ irreducible in $\mathbb{F}_2[x]$?
24626
Irreducibility of $X^n - 2$ over $\mathbf Z[i]$.
19968
Describe all $p^{n}$ (in terms of congruence conditions of $p$ and $n$) for which $x^{2}+1$ irreducible over $\mathbb{F}_{p^{n}}$.
85096
Let $K$ be a field and $f(x)\in K[x]$. Prove that $K[x]/(f(x))$ is a field if and only if $f(x)$ is irreducible in $K[x]$.
60816
Irreducibility of special cyclotomic polynomial.
151961
Irreducibility of $x^{p(p-1)}+x^{p(p-2)}+\cdots+x^p+1$ over $\mathbb Q$
102432
Irreducible polynomial of degree $8$
46429
Question about proof that $(a + b)^p = a^p+b^p$ in a field of characteristic $p$.
102422
Irreducibly of $x^5-x-1$ over $\mathbb{F}_3$