The correct answer is that there would have been 602,176 Crusaders, who could form themselves into a square 776 by 776; and after the stranger joined their ranks, they could form 113 squares of 5,329 men—that is, 73 by 73.
Or 113 × 732 - 1 = 7762.
This is a particular case of the so-called "Pellian Equation," respecting which see A. in M., p. 164.