Prove that if $p$ is prime then $\frac{X^p-1}{X-1}=X^{p-1}+\cdots+X+1$ is irreducbile in $\mathbb{Q}[X]$.
16035
Irreducibility of $X^{p-1} + \cdots + X+1$
95692
Factoring polynomials of the form $1+x+\cdots +x^{p-1}$ in finite field
76017
Prove that $x^3-2$ and $x^3-3$ are irreducible over $\Bbb{Q}(i)$
80144
Prove that $x-1$ divides $x^n-1$
100573
Show that $x^4-10x^2+1$ is irreducible over $\mathbb{Q}$
121479
Why is $X^4+1$ reducible over $\mathbb F_p$ with $p \geq 3,$ prime
10821
Using Eisenstein criterion show that $x^3+x^2-2x-1$ is irreducible?
34692
Prove if $ p$ is a prime of the form $3n+1$, then $p$ is also of the form $6m+1$
93196
$x^4 -10x^2 +1 $ is irreducible over $\mathbb Q$
81377
Show that $x^n + x + 3$ is irreducible for all $n \geq 2.$
114762
Prove that $f(x)$ is irreducible iff its reciprocal polynomial $f^*(x)$ is irreducible.
158106
Prove that 1 less than the number of equivalence classes divides $p-1$ where $p$ is prime
46951
For what values of $n > 1$ and a is $x^n - a$ irreducible in $\mathbb Q[x]$?
27942
showing that $n$th cyclotomic polynomial $\Phi_n(x)$ is irreducible over $\mathbb{Q}$
75123
If $p$ be a prime and r be any integer, $0 < r < p$ then $\frac{(p-1)!}{r!(p-r)!}$ is an integer.
146887
Prove that $f=x^4-4x^2+16\in\mathbb{Q}$ is irreducible
18336
$x^p-c$ has no root in a field $F$ if and only if $x^p-c$ is irreducible?