If $\frac{a^n-1}{b^n-1} $ is a natural number for every $n$ then $a = b^m$
97021
Do there exist two primes $p<q$ such that $p^n-1\mid q^n-1$ for infinitely many $n$?
24403
Prove that $ n < 2^{n}$ for all natural numbers $n$.
12100
$n \mid (a^{n}-b^{n}) \ \Longrightarrow$ $n \mid \frac{a^{n}-b^{n}}{a-b}$
1448
$x^a - 1$ divides $x^b - 1$ if and only if $a$ divides $b$
136304
Prove: $2^b-1\mid{}2^a-1 \iff b\mid{}a$
78471
Closure of $\{\frac{1}{n}\}:=M$
52672
Solution of $\frac{a}{b}=\frac{a'}{b'}$ if $a,b,a',b' \in \mathbb{N}$
77806
Proving if $a$ is not a multiple of prime $p$, then an integer $b$ exists such that $p^b - 1$ is a multiple of $a$
19046
Show that if $a$ and $b$ are positive integers with $(a,b)=1$ then $(a^n, b^n) = 1$ for all positive integers n
49166
$R^n \cong R^m$ iff $n=m$
10236
Show that $a^n \mid b^n$ implies $a \mid b$
84417
Prove that if $\gcd(a,b)=1$ then $\gcd(a^m, b)=1$
6012
Prove that $\gcd(a^n - 1, a^m - 1) = a^{\gcd(n, m)} - 1$
148455
Show that if $(a,n)=d>1$ and $k$ is any positive integer, then $a^k\not\equiv 1\pmod{n}.$
48839
Show that the order of $a\times b$ is equal to $nm$ if gcd(n,m)=1
90962
For positive integers $m,n$ if $\sqrt 7 - \frac{m}{n} > 0$ then prove that $\sqrt 7 - \frac{m}{n} > \frac{1}{{mn}}$
72511
If $n$ is an odd natural number, then $8$ divides $n^{2}-1$