History of Hindu Mathematics: A Source Book v2.c17.s23.20

v2.c17.s23.20

Now, one rational solution of (4m⁴ + n⁴)w² + 1 = x² is w &= 2r/((4m⁴ + n⁴) - r²), / x &= ((4m⁴ + n⁴) + r²)/((4m⁴ + n⁴) - r²). Therefore, we have the general solution of .x² + y² - 1 &= v² / x² - y² - 1 &= u²} as . x &= ((4m⁴ + n⁴) + r²)/((4m⁴ + n⁴) - r²), & u &= (2r(2m² + n²))/((4m⁴ + n⁴) - r²), / y &= 4mnr/((4m⁴ + n⁴) - r²), & v &= (2r(2m² - n²))/((4m⁴ + n⁴) - r²), } (A) where m, n, r are rational numbers.