History of Hindu Mathematics: A Source Book v2.c17.s17.t3.45

v2.c17.s17.t3.45

The following illustrative example and its solution are given :¹ $5x² + 16y² - 20 = z².$ Its solution is $x = ⅖vy + u,$ $z = 2uy + v;$ where 5u² - 20 = v². An obvious solution of this equation is given by u = 3, v = 5. Hence, we get a solution of the given equation as $x = 2y + 3,$ $z = 6y + 5.$ Therefore (x, y) = (5, 1), (7, 2), (9, 3),