Show that the polynomial $(x-1)(x-2) \cdots (x-n)-1$ is irreducible on $\mathbb{Z}[x]$ for all $n \geq 1$
106914
Existence of Irreducible polynomials over $\mathbb{Z}$ of any given degree
57884
Number of monic irreducible polynomials of prime degree $p$ over finite fields
48093
Irreducible polynomial in field extension
35959
irreducibility of a polynomial over $\mathbb{F}_2$
70249
Irreducibility of Polynomials in $k[x,y]$
40994
How to check that a cubic polynomial is irreducible?
151520
About the parity of the product $(a_1-1)(a_2-2)\cdots(a_n-n)$
121714
Show that the polynomial $X^5 + X^3 + \bar{1}$ in $(\mathbb{Z}/2\mathbb{Z}[X])$ is irreducible
124460
Show that if $f \in \mathbb{C} \left[x_1, \dots, x_n \right]$ vanishes at every point of $\mathbb{Z}^n$, then $f$ is the zero polynomial.
63605
Irreducible polynomials and affine variety
42265
A proof that $\displaystyle\sum_{i=1}^{n}P''(r_i)/P'(r_i)=0$ for a degree $n$ polynomial
52528
Showing that minimal polynomial has the same irreducible factors as characteristic polynomial
134701
Polynomials irreducible over $\mathbb{Q}$ but reducible over $\mathbb{F}_p$ for every prime $p$
114198
Showing that $y$ is irreducible in $\mathbb R[x,y]/(x^2+y^2-1)$.
100573
Show that $x^4-10x^2+1$ is irreducible over $\mathbb{Q}$
76017
Prove that $x^3-2$ and $x^3-3$ are irreducible over $\Bbb{Q}(i)$
32391
Show that $x^2+x+4$ is irreducible over $\mathbb Z_{11}$.