prove by induction; integer division by $5$ I'm having trouble with my math project.
 I have to prove that for very natural, $n$, there is an integer $q$ , and an integer $r$ such that:
$n=5q+r$   and $0\le r<5$   using induction
I have tried using the axiom of Archimedes but I can't really get around the problem. Sorry if this seems basic , I still have a really hard time with demonstrations 

For variety we prove it by strong iduction: $ $ if $\,n<5\,$ then $\ n = 0\cdot q+ n.\ $ Else $n\ge 5\,$ hence by strong induction $\, 0\le n\!-\!5 = 5q+r\,\ $ so $\ \,n = 5(q\!+\!1)+r. $
