History of Hindu Mathematics: A Source Book v2.c17.s14.126

v2.c17.s14.126

With an auxiliary equation like this the first integral solution of the equation Nx² + 1 = y² is x = ½αβ, y = ½(β² - 2); if α is even; or x = ½α(β² - 1), y = ½β(β² - 3); if β is odd.