History of Hindu Mathematics: A Source Book v2.c17.s18.t2.26

v2.c17.s18.t2.26

¹ Bibhutibhusan Datta has shown that this restriction is *not necessary*. In fact, starting with the assumption .y &= s(m²q²)/(n²p²), / x &= s(m²q²)/(n²p²) - 1;} m \geqslant n, q \geqslant p, and proceeding in the same way as above, he has obtained another solution of (A) in the form .y &= 2(m²q)/(n²p), & v &= m/n, / x &= 2(m²q)/(n²p) - 1, & u &= m/q(4(m²q)/(n²p) - 2).} (II) Datta finds two general solutions of (A), *viz.* .y &= (rm²q²)/(n²p²) + t, / x &= (rm²q²)/(tn²p²)((rm²q²)/(n²p²) - rq/p + t), / v &= rmq/np, / u &= m/nt((rm²q²)/(n²p²) + t)((rm²q²)/(n²p²) - rq/p + t);} (III)