Proof that a polynomial is irreducible for all $n \ne 4$.
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 $p$.
16592
Irreducible polynomial which is reducible modulo every prime
51952
Show that $x^{n-1}+\cdots +x+1$ is irreducible over $\mathbb Z$ if and only if $n$ is a prime.
127205
Explain proof of irreducibility of $x^{p-1} + 2x^{p-2}+ \dots +(p-1)x + p$
134701
Polynomials irreducible over $\mathbb{Q}$ but reducible over $\mathbb{F}_p$ for every prime $p$
78726
Prove via mathematical induction that $4n < 2^n$ for all $ n≥5$.
134726
Show the polynomial is irreducible in $\textbf Z_2$
48093
Irreducible polynomial in field extension
10627
When is $X^n-a$ is irreducible over F?
26336
Prove that $n(n^2 - 1)(n + 2)$ is divisible by $4$ for any integer $n$
132665
Show $p(X)$ (over a field) is irreducible iff $p(X+a)$ is irreducible
118916
How do I prove that a polynomial F[x] of degree n has at most n roots
97028
Find all irreducible monic polynomials in $\mathbb{Z}/(2)[x]$ with degree equal or less than 5
112427
Irreducibility of $p(x)=x^4-4x^2+8x+2$ over $\mathbb{Q}(\sqrt{-2})$- Dummit Foote Abstract algebra $9.4.10$
70386
Proof by induction: $2^n > n^2$ for all integer $n$ greater than $4$
121304
Is the set of polynomials of degree less than or equal to $n$ closed?