Prove that if $(a+b)$ divides $a^2$ then $(a+b)$ divides $b^2$ I'm trying to solve the following exercise: "Prove that if $(a+b)$ divides $a^2$ then $(a+b)$ divides $b^2$".
It's quite obvious how to prove divisibility for a product, but how to do it for a sum?

Hint:
$$a+b|(a+b)(a-b)=a^2-b^2$$
