“…Applying the Brahmagupta-Fibonacci identity from above, we get 4 2 + 6 2 + 6 2 + 9 2 = (9 − 4) 2 + (6 + 6) 2 = 5 2 + 12 2 = (9 + 4) 2 + (6 − 6) 2 = 13 2 + 0 2 = However, in this case, there are nine sums of four squares. (1,4,6,18), (1,6,12,14), (2,2,12,15), (2,6,9,16), (4,6,6,17), (4,6,10,15), (5,8,12,12), (6,6,7,16), (6,8,9,14) Only one of these is applicable to the Brahmagupta-Fibonacci identity, providing the two sum of two squares. A faster method, using a modified binary greatest common divisor, quickly validates a sum of four squares.…”