Prove that $a^n - b^n$ does not divide $a^n + b^n$
12694
Why does $a^n - b^n$ never divide $a^n + b^n$?
1478
An inequality for powers of reals: $a^{1/n}-b^{1/n}<(a-b)^{1/n}$
82953
In a ring with no zero-divisors, for $(m,n) =1$, $a^m = b^m$ and $a^n = b^n$ $\iff a =b$
156356
Proof that $x^n+\frac{1}{x^n}\in \mathbb Z$ by complete induction
12927
$A^2+B^2=AB$ and $BA-AB$ is non-singular
7894
Does it follow that $(n!)^n$ divide $(n^2)!$
98855
Prove $aba^{-1}b^{-1}\in{N}$ for all $a,b$
16642
Showing $a_n=\sin(n)$ does not converge
140405
Show that there does not exist any $n$ for which $a^n=a$ forall $a\in \Bbb Z_m$ where $m$ is divisible by the square of some prime.
135450
Prove $x^n$ is not uniformly convergent
97469
How to prove $|a^k|=n/\gcd(n,k)$ whenever $|a|=n$?
27281
How to prove $\,x^a-1 \mid x^b-1 \iff a\mid b$
98963
Prove that neither $A$ nor $B$ is divisible by $5$
20964
Proof that $n^2 < 2^n$
33866
Show that $n$ does not divide $2^n - 1$ where $n$ is an integer greater than $1$?
88995
Prove that $a^n-b^n = (a-b)(a^{n-1} + a^{n-2}b + \cdots + b^{n-1})$.
153313
Prove that for all integers $ a $ and $ b $, if $ a $ divides $ b $, then $ a^{2} $ divides $ b^{2} $.