Menu Close

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
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)
$${Let}\:{a}\:{and}\:{b}\:{be}\:{positive}\:{integers}\:{such} \\ $$$${that}\:{ab}+\mathrm{1}\:{divides}\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} .\:{Show}\:{that} \\ $$$$\frac{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} }{{ab}+\mathrm{1}}\:{is}\:{the}\:{square}\:{of}\:{an}\:{integer}. \\ $$$$\left({IMO}\:\mathrm{1988}\:{Qu}.\mathrm{6}\right) \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *