Hi,

I was hoping somebody could put me on the right line to prove this question. It says:

Let, $\displaystyle a, b, c$ be positive integers such that $\displaystyle \frac{a \sqrt{2} + b}{b \sqrt{2} + c}$ is a rational number. Prove that $\displaystyle a+b+c$ is a divisor of $\displaystyle a^2+b^2+c^2$

I'm never very good at proofs as I never know where to start. Would one times $\displaystyle \frac{a \sqrt{2} + b}{b \sqrt{2} + c}$ by $\displaystyle a+b+c$ and see what happens (I have but I can't see anything helpful)?

Thanks very much in advance for any help!