If $p \mid a^n$ then does $p^n \mid a^n$?
33714
$p$ prime, $p\mid a^k \Rightarrow p^k\mid a^k$
134348
When is $(p - 1)! + 1$ a power of $p$?
31465
Prove that if $a \mid b$ then $\gcd(a,b) = |a|$
158082
Is $\|A^n\|=\|A\|^n$ true for any normal operator in a Hilbert space?
96152
Showing that $a^n - 1 \mid a^m - 1 \iff n \mid m$
39217
If $d \mid n$ then $x^{q^d} - x \mid x^{q^n} - x$.
21006
Let $a,b$ be positive integers such that $a\mid b^2 , b^2\mid a^3 , a^3\mid b^4 \ldots$ so on , then $a=b$?
114667
$d\mid a,b \iff d\mid\gcd(a,b) \ $ [GCD Universal Property]
24572
Does $n \mid 2^{2^n+1}+1$ imply $n \mid 2^{2^{2^n+1}+1}+1$?
18693
If $a,b$ are positive integers such that $a^{n}+n$ divides $b^{n}+n$ for every $n$, then $a=b$
48211
When is $(a+b)^n \equiv a^n+b^n$?
81346
Let $r$ be the smallest positive integer such that $a^r \equiv 1 \bmod{n}$. Prove $r \mid \phi(n)$.
105180
When does $(ab)^n = a^n b^n$ imply a group is abelian?
115866
Proof by induction; $a^n$ divides $b^n$ implies $a$ divides $b$
138894
Prove that if $3\mid(a^2+b^2)$,then $3\mid a$ and $ 3\mid b$
82097
If $A \succeq B$, is it true that $B^{-1} \succeq A^{-1}$?
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 $a=b$