History of Hindu Mathematics: A Source Book v2.c17.s16.10

v2.c17.s16.10

Thus having known a single solution in positive integers of the equation Nx² ± c = y², says Brahmagupta, an infinite number of other integral solutions can be obtained by making use of the integral solutions of Nx² + 1 = y². If (p, q) be a solution of the former equation found empirically and if (α, β) be an integral solution of the latter then, by the Principle of Composition, $x = pβ ± qa, y = qβ ± Npa$ will be a solution of the former. Repeating the operations we can easily deduce as many solutions as we like.