# $\frac{(a^2+b^2)}{(1+ab)}$ must be a perfect square if it is an integer [duplicate]

Possible Duplicate:
Alternative proof that $(a^2+b^2)/(ab+1)$ is a square when it's an integer

I came across this problem, but couldn't solve it.

Let $a,b>0$ be two integers such that $(1+ab)\mid (a^2+b^2)$. Show that the integer $\frac{(a^2+b^2)}{(1+ab)}$ must be a perfect square.

It's a double star problem in Number theory (by Niven). Thanks in advance.

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## marked as duplicate by Zev ChonolesJun 26 '12 at 6:03

Let the double star come here too !! ;). I gave +1 and a star. Let me wait for another one.. –  Iyengar Jun 25 '12 at 10:35
Done. It's now a double star problem in math.SE ;-). –  JBC Jun 25 '12 at 10:43
@JBC : Ha ha, Yes.. –  Iyengar Jun 25 '12 at 10:43
–  anon Jun 25 '12 at 10:51
New and better solution without using vieta jumping method here math.stackexchange.com/questions/28438/… –  MathGod Jan 23 at 6:54