Proof for irreducibility of $x^p - x + a$ over $\mathbb{GF}(p)$
1487
How do I prove that $x^p-x+a$ is irreducible in a field with $p$ elements when $a\neq 0$?
18336
$x^p-c$ has no root in a field $F$ if and only if $x^p-c$ is irreducible?
121076
Show $x^p-t$ has no root in the field $\mathbb{F}_p(t)$
44403
Prove that $|a+b|^p \leq 2^p \{ |a|^p +|b|^p \}$
27942
showing that $n$th cyclotomic polynomial $\Phi_n(x)$ is irreducible over $\mathbb{Q}$
53012
Irreducibility of a polynomial if it has no root (Capelli)
44729
Prove $g$ is a generator if $g^q=1 \pmod p$
54192
Why $x^{p^n}-x+1$ is irreducible in ${\mathbb{F}_p}$ only when $n=1$ or $n=p=2$
25290
Determine the number of irreducible monic polynomials of degree 3 in $\mathbb F_p[x]$
60816
Irreducibility of special cyclotomic polynomial.
121658
$x^2+y^2-1$ irreducible in $\mathbb{Q}[x,y]$?
156859
Proving that $GF(p^n)$ contains a unique subfield isomorphic to $GF(p^m)$ if and only if $m$ is a divisor of $n$.
77620
Irreducible polynomials over $\mathbb Q$ and $\mathbb Z $
95594
Prove that a polynomial is irreducible or the field contains a $p$th root
46951
For what values of $n > 1$ and a is $x^n - a$ irreducible in $\mathbb Q[x]$?
76017
Prove that $x^3-2$ and $x^3-3$ are irreducible over $\Bbb{Q}(i)$
35959
irreducibility of a polynomial over $\mathbb{F}_2$