Question

prove that if x and y are both odd positive integers then x²+y² is even but not divisible by 4.​

Answer 1

Answer:

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 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. I am think I gave my best