Finding an irreducible polynomial in $\mathbb{Z}[x]$ such that it is reducible modulo 2,3 and 5.
16592
Irreducible polynomial which is reducible modulo every prime
121658
$x^2+y^2-1$ irreducible in $\mathbb{Q}[x,y]$?
154373
How many irreducible monic quadratic polynomials are there in $\mathbb{F}_p[X]$?
138275
Show $100+t$ is reducible in $\mathbb{Z}[[t]]$
57884
Number of monic irreducible polynomials of prime degree $p$ over finite fields
77620
Irreducible polynomials over $\mathbb Q$ and $\mathbb Z $
76640
Show that the polynomial $x^3-xy^2+y+1$ is irreducible in $\mathbb{Q}[x,y]$
27942
showing that $n$th cyclotomic polynomial $\Phi_n(x)$ is irreducible over $\mathbb{Q}$
120147
For what prime numbers $p$ is $x^2+x+1$ irreducible in $\mathbb{F}_p[X]$
53012
Irreducibility of a polynomial if it has no root (Capelli)
93291
Method for determining irreducibles and factorising in $\mathbb Z[\sqrt{d}]$
74777
Solvability and reducibility of a polynomial in a "chain" of finite fields
132572
Why this polynomial is irreducible?
39642
Efficient way to find $[\mathbb{Q}(\sqrt{5}, \sqrt{3}, \sqrt{2}): \mathbb{Q}(\sqrt{3}, \sqrt{2})]$
66960
Find a polynomial f(x) of degree 5 such that 2 properties hold.
10885
Existence of irreducible polynomials over finite field
96087
Let $\mathbb{F}_2 \cong \mathbb{Z}/2\mathbb{Z}$. Is $x^4+x^2+1$ irreducible in $\mathbb{F}_2[x]$?