How can I prove that $a^m-1|a^n-1 \Leftrightarrow m|n$?
96152
Showing that $a^n - 1 \mid a^m - 1 \iff n \mid m$
23590
Show that $\gcd\left(\frac{a^n-b^n}{a-b},a-b\right)=\gcd(n d^{n-1},a-b)$
22093
How to show $a^{2^n}+1 \mid a^{2^m}-1$?
80826
To prove $\left|\frac{p_n(z)}{q_m(z)}\right|\leq \frac{M}{|z|^{m-n}}$ for some $M>0$
43246
Showing that if $a<b$, then $a^{1/n} < b^{1/n}$
34059
$(a^{2^n}+1,a^{2^m}+1)=1 or 2$
71547
Prove $ 1+\left( 1-\frac{x}{n}\right)+...+\left(1-\frac{x}{n}\right)^{n-1}=\frac{n}{x}\left(1-\left(1-\frac{x}{n}\right)^n\right)$
39453
How do I prove that $S^n$ is homeomorphic to $S^m \Rightarrow m=n$?
18914
How prove this $A=\left(B-\frac{1}{110}I\right)^T\left(B+\frac{1}{110}I\right)$
145423
prove that if $1 \le m \le n$ then $\left(1+\frac1n\right)^m < 1+\frac mn + \left(\frac mn\right)^2$
83662
Prove that $ a $ divides $1^{a^{n}} + 2^{a^{n}} + ... + (a-1)^{a^{n}}$?
28136
$A^m\hookrightarrow A^n$ implies $m\leq n$ for a ring $A\neq 0$
45742
Prove that ${\left(\frac{x+1}{2}\right)}^{x+1} \leq x^x$
98855
Prove $aba^{-1}b^{-1}\in{N}$ for all $a,b$
9846
Prove $n-m \mid n^r - m^r\,$ [Factor Theorem, monomial case]
97469
How to prove $|a^k|=n/\gcd(n,k)$ whenever $|a|=n$?
93031
How to show that $\mathbb{Z}$ with the operation $m*n=m+(-1)^m n$ is associative?