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-

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)