- a,b and c are integers such that a|b and b|c. Prove that a^2 |(b^2 +bc).

if a|b than

$\displaystyle b = ma $ for some m in the integers

if b|c

$\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.