Mathematics in Ancient and Medieval India c7.s5.200

c7.s5.200

For the solution of 67x² + 1 = y², if 1, m be the solution then according to Bhāskara II's method k = m² - N i.e. if (1, 8) be an an arbitrary solution, then k = 8² - 67 = -3 Hence the first set can be written as : \begin{align*} &1)\ 67.1² - 3 = 8². Likewise the other sets are \\ &2)\ 67.5² + 6 = (41)² \\ &3)\ 67.\ (11)² - 7 = (90)² \\ &4)\ 67.\ (27)² - 2 = (221)² \\ &5)\ 67.\ (11934)² + 4 = (97684)² \\ &and 6)\ 67.(5967)² + 1 = (48842)² \end{align*}