Suppose a, b and n are positive integers. Prove that (a^n) | (b^n) if and only if a | b.
92975
Does $a^n \mid b^n$ imply $a\mid b$?
97469
How to prove $|a^k|=n/\gcd(n,k)$ whenever $|a|=n$?
21737
If $A|B$ and $B|A$ then prove $A=\pm B$
98855
Prove $aba^{-1}b^{-1}\in{N}$ for all $a,b$
76049
Prove that if $a|b$ and $a|c$ then $a|(sb+tc)$ for all $s, t \in \mathbb{Z}$
63651
If $(a,b)=1$ then there exist positive integers $x$ and $y$ s.t $ax+by=1$.
84946
If $0<a<b$, prove that $a<\sqrt{ab}<\frac{a+b}{2}<b$
90916
Prove that if $3\mid a^2+b^2$ then $3\mid a$ and $3\mid b$.
63183
Suppose $a,b,m,n$ are natural numbers, prove that if $a({m \over n})=b$ and $(a,n)=1$, then ${m \over n} \in \mathbb{N}$
64320
Prove that if $0<a<Pr(A)$ then there exists $B\subset A$ such that $Pr(B)=a$
88982
Prove that for any two sets $A$ and $B$, $A\notin B$ or $B\notin A$
132971
Prove that $|a| < b \iff -b<a<b$
24403
Prove that $ n < 2^{n}$ for all natural numbers $n$.
110256
Let $a,b \in {\mathbb{Z_+}}$ such that $a|b^2, b^3|a^4, a^5|b^6, b^7|a^8 \cdots$, Prove $a=b$
80255
How to prove that $|a-b|<\epsilon$ implies $|b|-\epsilon<|a|<|b|+\epsilon$?
115866
Proof by induction; $a^n$ divides $b^n$ implies $a$ divides $b$
127296
prove that a|b and b|a iff a=+-b