Prove that if x and y are odd positive integer then x^2+y^2 is even which is not divisible by 4

Prove that if x and y are odd positive integer then x^2+y^2 is even wh

1.	Prove that if x and y are odd positive integer then x^2+y^2 is even which is not divisible by 4
Answer» Let the two odd positive numbers be x = 2k + 1 a nd y = 2p + 1Hence x2\xa0+ y2\xa0= (2k + 1)2\xa0+ (2p + 1)2 = 4k2\xa0+ 4k + 1 + 4p2\xa0+ 4p + 1 = 4k2\xa0+ 4p2\xa0+ 4k + 4p + 2 = 4(k2\xa0+ p2\xa0+ k + p) + 2Clearly notice that the sum of square is even the number is not divisible by 4\xa0