Question

Prove if a and b are integers, prove that if a is even and b is even then a+b is even

Answer 1

Let a and b integers and suppose that are even numbers. Then, exist integers k and m such that
`a=2k` and
`b=2m`.

Then,

`a+b=2k+2m=2(k+m)=2n`

Since, k and m are integers then n=k+m is an integer. Then, since a + b is of the form 2 by an integer n, then a + b is an even number.