Question

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

Answer 1

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

Answer 2

a = 2, b =1

\[\frac{4 + 1}{1 +2} = \frac{5}{3}\]

Answer 3

Or, I didn't understand your question?

I don't think you will ever get a perfect square through that equation.

Answer 4

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

Answer 5

This is an IMO Problem.

Answer 6

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

Answer 7

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