History of Hindu Mathematics: A Source Book v2.c17.s23.41

v2.c17.s23.41

Therefore, the general solutions of .x² + y² + 1 &= u², / x - y² + 1 &= v²;} are .x &= (2m²)/(n²), & u &= (2m² + n²)/(n²), / y &= 2m/n, & v &= (2m² - n²)/(n²);} (a') .x &= 1/(n⁶)(32m⁶ + 6m²n⁴), / y &= 2m/(n⁵)(16m⁴ + n⁴), / u &= 1/(n⁶)(16m⁴ + n⁴)(2m² + n²), / v &= 1/(n⁶)(16m⁴ + n⁴)(2m² - n²);} (a'')