Proof that if $a^n|b^n$ then $a|b$
10236
Show that $a^n \mid b^n$ implies $a \mid b$
101159
Prove If a ≡ b (mod n) and c ≡ d (mod n), then a + c ≡ b + d (mod n)
109611
If G is a group, prove that $(ab)^n =a^nb^n$ implies G is abelian.
11867
Prove by induction that $n < 2^n$ for all $n \ge 1$
76049
Prove that if $a|b$ and $a|c$ then $a|(sb+tc)$ for all $s, t \in \mathbb{Z}$
138707
show that if $a | c$ and $b | c$, then $ab | c$ when $a$ is coprime to $b$.
36314
If $Ax = Bx$ for all $x \in C^{n}$, then $A = B$.
97469
How to prove $|a^k|=n/\gcd(n,k)$ whenever $|a|=n$?
138894
Prove that if $3\mid(a^2+b^2)$,then $3\mid a$ and $ 3\mid b$
118039
How prove $p!|(a+1)$ if $p!|a^p+1$
104344
Prove if $|a_{n+1}|/|a_n| \leq |b_{n+1}|/|{b_n}|$ and $\sum |b_n|$ is convergent, then $\sum |a_n|$ is convergent
88995
Prove that $a^n-b^n = (a-b)(a^{n-1} + a^{n-2}b + \cdots + b^{n-1})$.
13478
Prove that if $a^p-b^p$ is divisible by $p$, then it is also divisible by $p^2$
94516
If $3$ divides $a^2 + b^2$, then $3$ divides $a$ and $3$ divides $b$
113168
If $a > b$, is $a^2 > b^2$?
96152
Showing that $a^n - 1 \mid a^m - 1 \iff n \mid m$
90916
Prove that if $3\mid a^2+b^2$ then $3\mid a$ and $3\mid b$.