History of Hindu Mathematics: A Source Book v2.c17.s14.117

v2.c17.s14.117

(*i*) If k=± 1; then the auxiliary equation will be³ $Na²± 1=β²,$ where α, β are integers. Then by Brahmagupta's Corollary, we get x = 2αβ, y = β² + Na² as the required first solution in positive integers of the equation Nx² + 1 = y².