History of Hindu Mathematics: A Source Book v2.c17.s15.18

v2.c17.s15.18

It will be noticed that Nârâyaṇa does not expressly state that the value of the indeterminate multiplier *m* should be so chosen as will make |m² - N| least. It is perhaps particularly noteworthy that he recognised the relation b₁ = a₁n - k₁a. For b_1 &= (bn + Na)/k, / &= (n(a_1k - an) + Na)/k, [\because\ a_1k = an + b] / &= a_1n - ((n² - N)/k)a, / &= a_1n - k_1a, / \therefore a &= (a_1n - b_1)/k_1. Similarly, it will be found that b = (b₁n - Na₁)/k₁. For b₁n = a₁n² - k₁an,