Show that $x^{p^m} - x$ divides $x^{p^n} - x$ if and only if $m$ divides $n$.
1448
$x^a - 1$ divides $x^b - 1$ if and only if $a$ divides $b$
1487
How do I prove that $x^p-x+a$ is irreducible in a field with $p$ elements when $a\neq 0$?
77076
Proof that $(x-1)^2$ divides a $nx^{n+1} – (n+1)x^{n}+1$
143543
Prove that $(n - 1)^2 \mid n^k -1$ if and only if $(n - 1) \mid k$
39217
If $d \mid n$ then $x^{q^d} - x \mid x^{q^n} - x$.
124685
How to show $(mn)!$ is divisible by $(m!)^n$?
88181
Splitting field of $X^n-a$
26011
To show that $2$ | $x^{2n} - x^n$, $n \in \mathbb{Z^+}$ is the following adequate?
94516
If $3$ divides $a^2 + b^2$, then $3$ divides $a$ and $3$ divides $b$
115866
Proof by induction; $a^n$ divides $b^n$ implies $a$ divides $b$
21250
Prove $x \equiv a \pmod{p}$ and $x \equiv a \pmod{q}$ then $x \equiv a\pmod{pq}$
31331
$|a|=m,\,\gcd(m,n)=1 \implies a$ is an $n$'th power
156356
Proof that $x^n+\frac{1}{x^n}\in \mathbb Z$ by complete induction
83662
Prove that $ a $ divides $1^{a^{n}} + 2^{a^{n}} + ... + (a-1)^{a^{n}}$?
124131
Show that $(x-1)^2$ is a factor of $x^n -nx +n-1$
78416
Show that $7$ divides $a^{15}-a^3$ for any integer $a$
43059
Show that $g^k=e$ if and only if the order of $g$ is finite and divides $k$.