The relation $a^n|b^n$ implies that $a|b$, where $a$ and $b$ are positive integers and $n\ge1$.
10236
Show that $a^n \mid b^n$ implies $a \mid b$
30134
For $a,n \in \Bbb N$, how to prove if $a^n-1$ is prime then $a=2$ and $n$ is prime?
49372
$x+1/x$ an integer implies $x^n+1/x^n$ an integer
52357
If $a,b \in G$, show that $ab^{n}a^{-1}=(aba^{-1})^{n}$.
54430
For $a,b$ coprime, there exists positive integers $x,y$ such that $ax-by=1$
36602
$a^m=b^m$ and $a^n=b^n$ imply $a=b$
80009
Prove that $| |a|-|b| | \le |a-b|$
149287
Prove that $A,B>0$ and $A_{ij}0$
89792
Let $x,y$ be positive real numbers. Then $x<y$ iff $x^n<y^n$ for all $n\in \mathbb{N}$
148455
Show that if $(a,n)=d>1$ and $k$ is any positive integer, then $a^k\not\equiv 1\pmod{n}.$
88598
Property of $\{0^n, 1^n, \ldots\}$
2522
Why is $a^n - b^n$ divisible by $a-b$?
46831
Show that $ a，b, \sqrt{a}+ \sqrt{b} \in\mathbb Q \implies \sqrt{a},\sqrt{b} \in\mathbb Q $
105180
When does $(ab)^n = a^n b^n$ imply a group is abelian?
44897
Proof: If $n=ab$ then $2^a-1 \mid 2^n-1$
141102
If $a,b,c$ are positive integers, with $a^2+b^2-ab=c^2$ prove that $(a-b)(b-c)\le0$.
126280
In a P.I.D., if $a^m = b^m$ and $a^n = b^n$ for $m, n \in \mathbb{N}$ with $\gcd(m,n) = 1$, then $a=b$