$p$ is a prime number, $\, n\ge1 \, $and$ \, n \nmid p^n$.If $a \in GF(p)$, proof $x^{p^n}-x-a$ is reducible in $GF(p)$
54192
Why $x^{p^n}-x+1$ is irreducible in ${\mathbb{F}_p}$ only when $n=1$ or $n=p=2$
344
Prove that if $p\in \mathbb{Z}$ is irreducible, then it is also prime.
132665
Show $p(X)$ (over a field) is irreducible iff $p(X+a)$ is irreducible
46292
Find all primes $p>2$ for which $x^2+x+1$ is irreducible in $\mathbb{F}_p[x]$
130342
Show that for any integer a and prime p, $(a+1)^p \equiv a^p+ 1 \pmod{p}$.
46951
For what values of $n > 1$ and a is $x^n - a$ irreducible in $\mathbb Q[x]$?
152299
Proving $a^{n-1} \equiv 1 \mod n $ when n is not prime.
2614
Prove that , any primitive root $r$ of $p^n$ is also a primitive root of $p$
83291
Prove that $p(x)=(x-a)q(x)$ for some $q(x)\in R[x]$ of degree= (degree of $p)-1$.
95111
Elementary proof for $\sqrt{p_{n+1}} \notin \mathbb{Q}(\sqrt{p_1}, \sqrt{p_2}, \ldots, \sqrt{p_n})$ where $p_i$ are different prime numbers.
90533
Show that if $p(x)$ is reducible in $F[x]$, then $F[x]/(p(x))$ is not an integral domain.
39843
Let $P$ be a prime. Show that $\exists$ $x \in \mathbb{N}$ such that $f(x) = p$ then $\exists$ $y \in \mathbb{N}$ such that $g(y) = p$
107502
Let $p \geq 2$. Prove that if $2^p-1$ is prime then $p$ must also be prime.
43580
Let $p$ be a prime number and $G$ a non abelian group or order $p^3$. Prove that $Z(G) = [G,G]$.
6012
Prove that $\gcd(a^n - 1, a^m - 1) = a^{\gcd(n, m)} - 1$
121890
Proof that $ p $ | ${ p^n \choose k } $ for any prime $p$ and $ k < p^n$
120627
Reducibility of polynomials modulo p