Brahmagupta's problem

This problem was given in India by the mathematician Brahmagupta in 628 AD in his treatise Brahma Sputa Siddhanta:

solve the Pell's equation

${\displaystyle x^{2}-92y^{2}=1}$

for integers ${\displaystyle x,y>0}$.

Brahmagupta gave the smallest solution as

${\displaystyle (x,y)=(1151,120)}$.