Let the two odd positive numbers x and y be 2k + 1 and 2p + 1, respectively
i.e., x2 + y2 = (2k + 1)2 +(2p + 1)2
= 4k2 + 4k + 1 + 4p2 + 4p + 1
= 4k2 + 4p2 + 4k + 4p + 2
= 4 (k2 + p2 + k + p) + 2
Thus, the sum of square is even the number is not divisible by 4
Therefore, if x and y are odd positive integer, then x2 + y2 is even but not divisible by four.
Hence Proved