
division proof help
 a,b and c are integers such that ab and bc. Prove that a^2 (b^2 +bc).
if ab than
$\displaystyle b = ma $ for some m in the integers
if bc
$\displaystyle c = nb $ for some n in the integers,
I know I need to show that if $\displaystyle a^{2}  (b^{2} + bc) $
than
$\displaystyle b^{2} + bc = k a^{2} $ for some k in integers.
$\displaystyle b^{2} + bc = m^{2}a^{2} + ma nb $
really stuck from here, not such if my working is correct so far either,
any help appreciated.

Re: division proof help
Try substituting $\displaystyle ma$ for b in your last equation on the right side