History of Hindu Mathematics: A Source Book v2.c17.s17.t5.15

v2.c17.s17.t5.15

Since the given equation is homogeneous, any multiple of these values of x, y, z will also be its solution. Therefore, multiplying by 8λ p² n², we get the following solution of the equation p²x² + bxy + cy² = z² in integers : .x &= m² (4cp² - b²) - 4\lambda²p²n² - 4\lambda bmn, / y &= 8\lambda mnp², / z &= m² (4cp² - b²) + 4\lambda²p²n²,} (5.2) where m, n, are arbitrary integers.