History of Hindu Mathematics: A Source Book v2.c17.s23.16

v2.c17.s23.16

For a rational value of y, 2pq must be a square. So we take p = 2m², q = n². Hence we have the assumption .x² &= (4m⁴ + n⁴)w² \mp 1, / y² &= 4m²n²w²;} \eqno{(2)} the upper sign being taken for Case *i* and the lower sign for Case *ii*.