Find integer solutions to x^2 - 92y^2 = 1.

x=1        y=0
x=1151     y=120
x=2649601  y=276240
etc.

Each successive solution is about 2300 times the previous
solution;  they are every 8th partial fraction (x=numerator,
y=denominator) of the continued fraction for sqrt(92) = 
[9,  1,1,2,4,2,1,1,18,  1,1,2,4,2,1,1,18,  1,1,2,4,2,1,1,18, ...]

Once you have the smallest positive solution (x1,y1) you
don't need to "search" for the rest.  You can obtain the nth positive
solution (xn,yn) by the formula

(x1 + y1 sqrt(92))^n = xn + yn sqrt(92).

See Niven & Zuckerman's An Introduction to the Theory of Numbers.
Look in the index under Pell's equation.