Existence of Irreducible polynomials over $\mathbb{Z}$ of any given degree
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.
84355
Methods to see if a polynomial is irreducible
38419
Existence of Polynomial with whom product contains only prime powers
129109
Is the set of polynomial with coefficients on $\mathbb{Q}$ enumerable?
129834
Show that there is a unique polynomial of degree at most $2n+1$ such that $q^{[k]}(x_1)=a_k,$ $q^{[k]}(x_2)=b_k$ for $k=0, \dots, n$.
24626
Irreducibility of $X^n - 2$ over $\mathbf Z[i]$.
91356
Irreducibility of an infinite sequence of polynomials
40994
How to check that a cubic polynomial is irreducible?
121658
$x^2+y^2-1$ irreducible in $\mathbb{Q}[x,y]$?
78540
Every irreducible polynomial f over perfect field F is separable
104782
Polynomial irreducible - maximal ideal
58490
Polynomials, finite fields and cardinality/dimension considerations
100573
Show that $x^4-10x^2+1$ is irreducible over $\mathbb{Q}$
44878
Factor $x^5+x^2+1$ into irreducible polynomials in $Z[x]$
65558
Irreducible in $\mathbb{Z}[\sqrt{-5}]$
146591
Inseparable polynomial over a non-perfect field