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
 * $$x^2 - 92y^2 = 1$$

for integers $$x,y>0$$.

Brahmagupta gave the smallest solution as
 * $$(x,y) = (1151,120)$$.