Prove that $a^n$ divides $b^n$ implies that $a$ divides $b$.
115866
Proof by induction; $a^n$ divides $b^n$ implies $a$ divides $b$
50534
Prove that if $n^2$ is divided by 3, then also $n$ can also be divided by 3.
27449
Product of Divisors of some $n$ proof
86030
Prove or disprove - If a divides b and b divides a does a=b
89175
Proof of $(a+b)^{n+1}$
26514
Prove that if $n$ is a composite, then $2^n-1$ is composite.
88662
$n$ divides $\phi(a^n -1)$ where $a, n$ are positive integer.
69967
How to prove $\gcd(a^m-b^m,a^n-b^n) = a^{\gcd(m,n)} - b^{\gcd(m,n)} $?
138894
Prove that if $3\mid(a^2+b^2)$,then $3\mid a$ and $ 3\mid b$
19202
$\mathbb{F}_{p^d}\subseteq\mathbb{F}_{p^n}$ if and only if $d$ divides $n$
84733
Why $a\equiv b\pmod n$ implies $a$ and $b$ have equal remainder when divided by $n$?
75373
Show that $2^n>n$ for $n\in \mathbb{N}$
7491
How to show that $7\mid a^2+b^2$ implies $7\mid a$ and $7\mid b$?
44897
Proof: If $n=ab$ then $2^a-1 \mid 2^n-1$
75199
$a \equiv b \pmod n$ and $c\equiv d \pmod n$ implies $ac \equiv bd \pmod n$
127293
Prove that $(a-b) \mid (a^n-b^n)$
109611
If G is a group, prove that $(ab)^n =a^nb^n$ implies G is abelian.