$X^4-10X+1$ reducible in $\mathbb{F}_p[X]$ for all prime $p$
120627
Reducibility of polynomials modulo p
138275
Show $100+t$ is reducible in $\mathbb{Z}[[t]]$
46292
Find all primes $p>2$ for which $x^2+x+1$ is irreducible in $\mathbb{F}_p[x]$
130342
Show that for any integer a and prime p, $(a+1)^p \equiv a^p+ 1 \pmod{p}$.
38419
Existence of Polynomial with whom product contains only prime powers
152109
In a UFD if $x$ is irreducible, then $(x)$ is prime
140497
Irreducibles are prime in a UFD
10514
Proof that no polynomial with integer coefficients can only produce primes
77240
Show that $4 + \sqrt{10}$ is not prime in $\mathbb{Z}\bigl [\sqrt{10}\bigr]$
154360
Show $f$ can't be irreducible over a finite field if $f^\prime$ is the zero polynomial.
46821
Finding roots in $\mathbb{Z}_p$
80188
There are infinitely many irreducible polynomials in $\Bbb{F}_p[X]$
73997
$x^{p-1} + ... + x^2 + x + 1$ is irreducible using Eisenstein's criterion?
103552
The minimal polynomial of a primitive $p^{m}$-th root of unity over $\mathbb{Q}_p$
126808
Is it true that if $f(x)$ has a linear factor over $\mathbb{F}_p$ for every prime $p$, then $f(x)$ is reducible over $\mathbb{Q}$?
100573
Show that $x^4-10x^2+1$ is irreducible over $\mathbb{Q}$
1487
How do I prove that $x^p-x+a$ is irreducible in a field with $p$ elements when $a\neq 0$?