Let a and b be positive integers such that ab+1 divides a^2 +b^2 . Show that ((a^2 +b^2 )/(ab+1)) is the square of an integer. (IMO 1988 Qu.6)


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Question Number 7213 by Yozzia last updated on 16/Aug/16

$L e t a a n d b b e p o s i t i v e i n t e g e r s s u c h$ $t h a t a b + 1 d i v i d e s a^{2} + b^{2} . S h o w t h a t$ $\frac{a^{2} + b^{2}}{a b + 1} i s t h e s q u a r e o f a n i n t e g e r .$ $(I M O 1988 Q u . 6)$
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