## anonymous 4 years ago Prove that :If a,b belongs to Z then (a^2 + b^2)/(1 + ab) is a perfect square.

1. anonymous

I know the answer......I just want to confirm it.

2. anonymous

a = 2, b =1 $\frac{4 + 1}{1 +2} = \frac{5}{3}$

3. anonymous

Or, I didn't understand your question? I don't think you will ever get a perfect square through that equation.

4. anonymous

Try b = 0 you get one . Now how do I prove it?

5. anonymous

This is an IMO Problem.

6. anonymous

But I think that's it, it's only valid when b=0. Do you have any other example?

7. anonymous

$\frac{a^2+b^2}{1+ab} = q^2$ $\sqrt{\frac{a^2+b^2}{1+ab}} = q$Now we need some manipulation here.