Prove that if x and y are odd positive integers, then x2 +y2 is even but not divisible by 4

Prove that if x and y are odd positive integers, then x2 +y2 is even b

1.	Prove that if x and y are odd positive integers, then x2 +y2 is even but not divisible by 4
Answer» Thanks Let the two odd positive no. be x = 2k + 1 and y = 2p + 1Hence, x2\xa0+ y2 = (2k + 1)2\xa0+(2p + 1)2 = 4k2\xa0+ 4k + 1 + 4p2\xa0+ 4p + 1 = 4k2\xa0+ 4p2\xa0+ 4k + 4p +\xa02 = 4 (k2\xa0+ p2\xa0+ k + p) + 2\xa0clearly, notice that the sum of square is even the no. is not divisible by 4hence, if x and y are odd positive integer, then x2\xa0+ y2\xa0is even but not divisible by four Shut up re