History of Hindu Mathematics: A Source Book v2.c17.s15.13

v2.c17.s15.13

a_1 &= (an + b)/k, \\ b_1 &= (bn + Na)/k, \\ k_1 &= (n² - N)/k. \end{aligned} The numbers a₁, b₁, k₁ are all integral. The equation (2) then becomes Na₁² + k₁ = b₁². 3 Proceeding exactly in the same way, we can obtain from (3) a new equation of the same kind, Na₂² + k₂ = b₂², where again a₂, b₂, k₂ are whole numbers. By repeating the process, we shall ultimately arrive at an equation, states Bhâskara II, in which the interpolator k will reach the value ± 1, ± 2 or ± 4, and in which (a, b) will be integers.