Prove that $p(x)=(x-1)(x-2) \cdots (x-n) + 1$ is irreducible over $\mathbb{Z}$ for all $n \geq 1$, $n \neq 4$.
53669
Prove that the polynomial $(x-1)(x-2)\cdots(x-n) + 1$, $ n\ge1 $, $ n\ne4 $ is irreducible over $\mathbb Z$
70523
Proving that $x^4 - 10x^2 + 1$ is not irreducible over $\mathbb{Z}_p$ for any prime $p$.
83291
Prove that $p(x)=(x-a)q(x)$ for some $q(x)\in R[x]$ of degree= (degree of $p)-1$.
33011
Prove that the polynomial $f_n(x)=nx^{n+1}-(n+1)x^n+1$ is divisible by $(x-1)^2$
26069
Why is $X^4-16X^2+4$ irreducible in $\mathbb{Q}[X]$?
97028
Find all irreducible monic polynomials in $\mathbb{Z}/(2)[x]$ with degree equal or less than 5
114812
Let $p(z)=z^n+a_{n-1}z^{n-1}+a_{n-2}z^{n-2}+...+a_0$ be a complex polynomial satisfying $|p(z)| \leq 1$ for $|z|\leq 1$, then prove that $p(z)=z^n$
127205
Explain proof of irreducibility of $x^{p-1} + 2x^{p-2}+ \dots +(p-1)x + p$
140808
Problem on Galois theory and irreducible polynomial
12166
How many irreducible polynomials of degree $n$ exist over $\mathbb{F}_p$?
6943
Idea behind proof that $\frac{21n+4}{14n+3}$ is irreducible for all $n$
31215
Irreducible cyclotomic polynomial
112427
Irreducibility of $p(x)=x^4-4x^2+8x+2$ over $\mathbb{Q}(\sqrt{-2})$- Dummit Foote Abstract algebra $9.4.10$
38364
Showing that $x^n -2$ is irreducible in $\mathbb{Q}[X]$
27577
An irreducible polynomial of degree coprime to the degree of an extension is irreducible over this extension
134701
Polynomials irreducible over $\mathbb{Q}$ but reducible over $\mathbb{F}_p$ for every prime $p$
64878
Is this polynomial irreducible in $\mathbb{Q}$?