Question

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

Answer 1

Let the two odd numbers be

(2a+1) & (2b+1) because if we add 1 to any even no. it will be odd.

x²+y²

=>(2a+1)²+(2b+1)²

=>(4a²+4a+1)+(4b²+4b+1)

=>4(a²+b²+a+b)+2

4 Is not a multiple of 2 it means clearly that 4 is not multiple of x²+y² , so x²+y² is even but not divisible by 4.

Hence proved

Answer 2

X=3, y=5 because x

${x}^{2} = {3}^{2} = 9 \\ 9 + 5 = 14 \\ it \: is \: even \: number \: but \: not \: divisible \: by \: 4$