# division proof help

• January 27th 2014, 06:20 AM
Tweety
division proof help
1. a,b and c are integers such that a|b and b|c. Prove that a^2 |(b^2 +bc).

if a|b than

$b = ma$ for some m in the integers

if b|c

$c = nb$ for some n in the integers,

I know I need to show that if $a^{2} | (b^{2} + bc)$

than

$b^{2} + bc = k a^{2}$ for some k in integers.

$b^{2} + bc = m^{2}a^{2} + ma nb$

really stuck from here, not such if my working is correct so far either,

any help appreciated.
• January 27th 2014, 11:31 AM
Try substituting $ma$ for b in your last equation on the right side