Prove if $a^n|b^n$ then $a|b$
92975
Does $a^n \mid b^n$ imply $a\mid b$?
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 $a=b$
94516
If $3$ divides $a^2 + b^2$, then $3$ divides $a$ and $3$ divides $b$
44403
Prove that $|a+b|^p \leq 2^p \{ |a|^p +|b|^p \}$
132971
Prove that $|a| < b \iff -b<a<b$
88982
Prove that for any two sets $A$ and $B$, $A\notin B$ or $B\notin A$
20110
How to prove $(AB)^T=B^T A^T$
138894
Prove that if $3\mid(a^2+b^2)$,then $3\mid a$ and $ 3\mid b$
1478
An inequality for powers of reals: $a^{1/n}-b^{1/n}<(a-b)^{1/n}$
17176
Proof that $x^n \mod b = (x \mod b)^n$
138212
Please help me prove: $v(a+b)\leq v(a)+v(b)$, and $v(ab)\leq v(a)v(b)$ where $v(x)=\inf{\{\vert x^n \vert}^{1/n}: n\in\mathbb{N}\}$
48081
Prove that for all $n \in \mathbb{N}$: $2^{n-1}(a^n + b^n) \ge (a + b)^n$
48484
Prove that $6|a+b+c$ if and only if $6|a^3+b^3+c^3$
88995
Prove that $a^n-b^n = (a-b)(a^{n-1} + a^{n-2}b + \cdots + b^{n-1})$.
130093
Prove by Induction : $n < 2^n$
11867
Prove by induction that $n < 2^n$ for all $n \ge 1$
96152
Showing that $a^n - 1 \mid a^m - 1 \iff n \mid m$