Prove that there exists an irreducible polynomial $f\in\mathbb{F}_p[x]$ of degree $2014$
10885
Existence of irreducible polynomials over finite field
38419
Existence of Polynomial with whom product contains only prime powers
16035
Irreducibility of $X^{p-1} + \cdots + X+1$
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 $\mathbb{Q}[x,y]$?
118950
Irreducibility criteria for polynomials with several variables.
140808
Problem on Galois theory and irreducible polynomial
133312
Are these polynomials irreducible in $\mathbb{Q}[x]$?
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 $k=0, \dots, n$.
83036
f(g(x)) has a degree divisible by n
27577
An irreducible polynomial of degree coprime to the degree of an extension is irreducible over this extension
109610
Is $\mathbb{R}[X]/(P)$ isomorphic to $\mathbb C$ for every irreducible polynomial $P$ of degree $2?$
132665
Show $p(X)$ (over a field) is irreducible iff $p(X+a)$ is irreducible
10627
When is $X^n-a$ is irreducible over F?
73344
Definition of irreducible polynomial via the units of an integral domain.
148909
Irreducible polynomials of degree 3 and 5
70537
Irreducible polynomials have distinct roots?