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» x and y are odd integers. So they should be of the form x= 2m+1, y= 2n+1 for some integers m and n.x^2 + y^2 =(2m+1)^2 + (2n+1)^2=4m^2+4m +1+4n^2+4n+1=4m^2+4n^2+4m+4n+2=4(m^2+n^2+m+n) + 2Which is an even number but not divisible by 4.