Question

Prove algebraically that the difference between any two different odd numbers is an even number.

Thanks.

Answer 1

an odd number is of the form 2k+1 where k is any integer. So, subtracting 2m+1 from 2n+1 you get

(2n+1)-(2m+1)
= 2n+1-2m-1
= 2n+2m
= 2(n+m)

any multiple of 2 is even