History of Hindu Mathematics: A Source Book v2.c17.s15.10

v2.c17.s15.10

Suppose we have an equation of the form $Na² + k = b²,1$ where a, b, k are simple integers, relatively prime, k being positive or negative. Then by Bhâskara's Lemma $N((am+b)/k)² + (m²-N)/k = ((bm+Na)/k)²,2$ where m is an arbitrary integral number. In the above rule, m has been styled the indeterminate multiplier. Now, by means of the pulveriser, its value is determined so that $(am+b)/k is a whole number.$