Proving that $X^n-a$ is irreducible if $a$ is no $p$-th power for any prime $p$ dividing the degree diving the degree
10627
When is $X^n-a$ is irreducible over F?
146887
Prove that $f=x^4-4x^2+16\in\mathbb{Q}$ is irreducible
121479
Why is $X^4+1$ reducible over $\mathbb F_p$ with $p \geq 3,$ prime
46741
Prove that $n$ divides $\phi(a^n -1)$ where $a, n$ are positive integer without using concepts of abstract algebra
46572
Degree of a splitting field is no greater than $n!$
25471
Irreducibility of $x^n-x-1$ over $\mathbb Q$
97729
Show that a polynomial $f(x)$ over a field $k$ is irreducible if and only if the polynomial $f(x+1)$ is irreducible
83036
f(g(x)) has a degree divisible by n
28658
$R$ with an upper bound for degrees of irreducibles in $R[x]$
12166
How many irreducible polynomials of degree $n$ exist over $\mathbb{F}_p$?
40994
How to check that a cubic polynomial is irreducible?
57884
Number of monic irreducible polynomials of prime degree $p$ over finite fields
6943
Idea behind proof that $\frac{21n+4}{14n+3}$ is irreducible for all $n$
44502
An irreducible polynomial cannot share a root with a polynomial without dividing it
4706
Prove $f=x^p-a$ either irreducible or has a root. (arbitrary characteristic) (without using the field norm)
120627
Reducibility of polynomials modulo p
40502
The Degree of Zero Polynomial.