If $a,b >1$ prove that $a$ divides $b$ iff $m\_i\leq n\_i$ for $1\leq i\leq r$.
(Exponents ${n\_i}$ with $r+1 \leq i \leq s$, if there are any, are unrestricted)

where $a = \prod\_{i=1}^{r}p\_i^{m\_i}$ and $b = \prod\_{i=1}^{s}p\_i^{n\_i}$

$sp(a)$ = {$p\_1,p\_2,...,p\_r$} and $sp(b)$ = {$p\_1,p\_2,...,p\_s$} with $r \leq s$

I am really stuck at this one. If anyone knows how to prove this, please help me.

Thanks!