If $a^m-1 \mid a^n -1$ then $m \mid n$
96152
Showing that $a^n - 1 \mid a^m - 1 \iff n \mid m$
83307
If $n\mid a^2-1$, $n$ an odd integer, show $n = \gcd(a-1, n)\gcd(a+1, n)$
35945
Proof that if $\gcd(a,b) = 1$ and $a\mid n$ and $b\mid n$, $ab \mid n$
83407
How to show that that $q \mid p-1$?
5981
For which values of $a$ does $a-2 \mid a^3+4$
28136
$A^m\hookrightarrow A^n$ implies $m\leq n$ for a ring $A\neq 0$
4141
Prove: If $a\mid m$ and $b\mid m$ and $\gcd(a,b)=1$ then $ab\mid m$
77164
If $a \mid m$ and $(a + 1) \mid m$, prove $a(a + 1) | m$.
78031
$c\mid a,b\iff c\mid\gcd(a,b)$ [GCD Universal Property]
100558
Prove that for any even positive integer $n$, $n^2-1 \mid 2^{n!}-1$
27281
How to prove $\,x^a-1 \mid x^b-1 \iff a\mid b$
147902
Prove $a \mid m$ and $b \mid m \implies \frac{a \cdot b}{\text{gcd}(a, b)} \mid m$
22093
How to show $a^{2^n}+1 \mid a^{2^m}-1$?
152299
Proving $a^{n-1} \equiv 1 \mod n $ when n is not prime.
62474
If $AB=I_n$ and $BA=I_m$ then $n=m$.
82953
In a ring with no zero-divisors, for $(m,n) =1$, $a^m = b^m$ and $a^n = b^n$ $\iff a =b$
1448
$x^a - 1$ divides $x^b - 1$ if and only if $a$ divides $b$