If $m\mid n$ then $p^m-1\mid p^n-1$
96152
Showing that $a^n - 1 \mid a^m - 1 \iff n \mid m$
43246
Showing that if $a<b$, then $a^{1/n} < b^{1/n}$
141088
Proof : $2^{n-1}\mid n!$ if and only if $n$ is a power of $2$.
134365
When is this true: If $m^2$ is a multiple of N then m is a multiple of N
95000
Using induction to prove that $2 \mid (n^2 − n)$ for $n\geq 1$
131551
$pq\mid pn^q+qn^p+kn$ for some $k,\,$ if $p,q$ are primes
78852
If $\gcd(m,n) =1, $ then $m\mathbb{Z}/ mn\mathbb{Z} \cong \mathbb{Z}/(n)$
32166
Prove: if $n\mid 7^n+6^n$ and $n>1$, then $13\mid n$
106401
Prove: $p-mq | f(m)$ where $m$ is any integer
151692
When does $2^n-1$ divide $3^n-1$?
22093
How to show $a^{2^n}+1 \mid a^{2^m}-1$?
145041
Given that $p$ is a prime and $p\mid a^n$, prove that $p^n\mid a^n$.
18018
Proving that $4 \mid m - n$ is an equivalence relation on $\mathbb{Z}$
118629
$p,q$ odd primes, $q\mid a^p-1\Rightarrow q\mid a-1$ or $\,2p\mid q-1$
33714
$p$ prime, $p\mid a^k \Rightarrow p^k\mid a^k$
97021
Do there exist two primes $p<q$ such that $p^n-1\mid q^n-1$ for infinitely many $n$?
83407
How to show that that $q \mid p-1$?