Mathematics in Ancient and Medieval India c7.s5.208

c7.s5.208

If KK¹ be a perfect square, $x = (ab¹¹b)/(√(KK¹)), y = ± (bb¹¹)/(√(KK¹)) are rational$ solutions of Nx² + 1 = y². If KK¹ be not a perfect square, the relation (2) is to be replaced by relation (1). In particular, if we put K = K¹, the roots become (ab)/K and ± (b²²)/K. The lower sign gives the root (0, ± 1) which must be left out of consideration.