Prove that the sum of two odd numbers is an even number

Let a and b be odd number.

Because they are odd, by definition:

a = 2n + 1

b = 2m + 1

If we add them up:

a + b = 2n + 1 + 2m + 1

= 2n + 2m + 2

= 2 (n + m + 2)

= 2k where k = n + m + 2

therefore a + b is always even.