# Math Help - division algorithm problem

1. ## division algorithm problem

i'm not sure how to even approach this problem. any help?

Suppose $a,b,q,r e Z$ such that $a=bq+r$, $b>0$ and $0<=r. then $q=[a/b]$ and $r=a-b[a/b]$

(Hint. Use the uniqueness of the division algorithm).

Suppose $a,b,q,r e Z$ such that $a=bq+r$, $b>0$ and $0<=r. then $q=[a/b]$ and $r=a-b[a/b]$
$a=bq+r \implies \frac{a}{b} = q + \frac{r}{b}$.Since $0 \leq r < b$, $q = \left[\frac{a}{b}\right]$