Prove or disprove the inequality Let $d,\ a,\ x,\ b,\ y $ be integers. $d$ divides $a$ and $b$.
The question is:  Assume $ax + by \gt 0$. Prove or disprove : $d \le ax + by $
I know that $d | ax+by$, but I can't figure out the proof for why $d$ would be $\le ax+by$.

$d| (ax+by)  $ so that $$ ax+by=dn$$ If $ ax+by >0$, then $$n\neq 0,\ ax+by=|dn| \geq d $$ 
