Let $k, m, n \in\mathbb Z^+$, where $k$ and $m$ are relatively prime. Prove that if $k|mn$ then $k|n$ .
Suppose $a,b,m,n$ are natural numbers, prove that if $a({m \over n})=b$ and $(a,n)=1$, then ${m \over n} \in \mathbb{N}$