Question

prove that if x and y are both odd positive integer then X square + Y square is even but not divisible by 4​

Answer 1

$\mathbb{SOLUTION-}$

As we know a odd positive integer exists in the form 2q+1

S0, let x = 2m+1 and y = 2n+1

x²+y² = (2m+1)² + (2n+1)²

         = 4m² + 4m+1 +4n²+4n+1

          = 4m²+4n²+4m+4n+2

           = 4(m²+n²+m+n) +2

            = 4 k + 2 ( where k = m²+n²+m+n)

Here,

It is even since it has 2 as remainder and it is not divisible by 4 as it has 2 as remainder