Question

Prove that if m^2 - n^2 is even, then m - n is even also.

Answer 1

Explanation:

Given

`m^2-n^2` is even i.e.

it is a multiple of 2

let us suppose it 2k

and we know that it is possible only when either both m&n is odd or even

i.e.

`\left ( even\right )^2-\left ( even\right )^2`=even number

`\left ( odd\right )^2-\left ( odd\right )^2`=odd number

thus m-n is even for both case i.e. for both m&n either odd or even