Prove $\frac{X^p-1}{X-1}$ for $p$ prime is irreducible in $\mathbb{Q}[X]$
16035
Irreducibility of $X^{p-1} + \cdots + X+1$
24626
Irreducibility of $X^n - 2$ over $\mathbf Z[i]$.
64878
Is this polynomial irreducible in $\mathbb{Q}$?
133312
Are these polynomials irreducible in $\mathbb{Q}[x]$?
111935
Irreducible but not prime
146887
Prove that $f=x^4-4x^2+16\in\mathbb{Q}$ is irreducible
114762
Prove that $f(x)$ is irreducible iff its reciprocal polynomial $f^*(x)$ is irreducible.
116856
Proving that a polynomial of the form $(x-a_1)\cdots(x-a_n) + 1$ is irreducible over $\mathbb{Q}$
121714
Show that the polynomial $X^5 + X^3 + \bar{1}$ in $(\mathbb{Z}/2\mathbb{Z}[X])$ is irreducible
25471
Irreducibility of $x^n-x-1$ over $\mathbb Q$
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 $\mathbb{Q}$?
78143
Proving $\mathbb{F}_p/\langle f(x)\rangle$ with $f(x)$ irreducible of degree $n$ is a field with $p^n$ elements
35959
irreducibility of a polynomial over $\mathbb{F}_2$
100573
Show that $x^4-10x^2+1$ is irreducible over $\mathbb{Q}$
44600
How can I prove: if $p $ is prime and $n>1$, then $ p^{\frac1n} $ is irrational?
154360
Show $f$ can't be irreducible over a finite field if $f^\prime$ is the zero polynomial.
10821
Using Eisenstein criterion show that $x^3+x^2-2x-1$ is irreducible?