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

Answer:

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.