Question

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

Answer 1

Hi mate here is the answer:-✍️✍️

Correct question is=>

Question:

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

Answer:

Let us consider two odd positive integers x =

2m + 1 and y = 2n + 1

Then,

x2 + y2 = (2m + 1)2 + (2n + 1)2

Squaring these terms using (a + b)2 = a2 + 2ab + b2

⇒ x2 + y2 = 4m2 + 1 + 4m + 4n2 + 1 + 4n

⇒ x2 + y2 = 4(m + n)2 + 4(m + n) + 2 which is even, as each term is divisible by 2

But not divisible by 4, as 3rd term is 2 which is not divisible by 4

Hope it helps you ❣️☑️☑️☑️