Prove that if `xa n dy` are odd positive integers, then `x^2+y^2` is even but not divisible by 4.

Explanation

Let x=2m+1 and y=2m+3 are odd integers, for every positive integers, for every positive integer m,
Then, `x^(2)+y^(2)(2m+1)^(2)+(2m+3)^(2)`
`=4m^(2) =(2m+1)^(2)+(2m+3)^(2)`
`=4m^(2)+1+4m+4m^(2)+9+12m [therefore (a+b)^(2)=a^(2)+2ab+b^(2)]`
`=8m^(2)+16m+10="even"`
`=2(4m^(2)+8m+5) or 4(2m^(2)+4m+2)+1`
Hence, `x^(2)+y^(2)` is even for every positive integer m but not divisible by 4.