Explanation:
650065 = (a² + 1)(c² + 1)
and
650065 = (ac - 1)² + (a + c)² = the sum of 2 squared numbers (ac - 1)² and (a + c)².
we see that 5 and 13 and therefore 5×13=65 are all factor of 650065. and then 650065/65 = 10001.
and we know that 65 = (64 + 1) = (8² + 1)
and 10001 = (10000 + 1) = (100² + 1)
so, a = 8, c = 100
that means the 2 squared numbers summing up to 650065 are
(ac - 1)² = (8×100 - 1)² = 799² = 638,401
(a + c)² = (8 + 100)² = 108² = 11,664
650,065 = 638,401 + 11,664 = 799² + 108²