Question

Prove that the sum of two odd numbers is even.

Answer 1

Let $x$ and $y$ be two odd numbers.

Then $x=2m+1$ for some natural number $m$ and $y=2n+1$ for some natural number $n$.

Lets take out their sum.

Thus $x+y=2m+1+2n+1=2(m+n+1)$

Here with the addition $2$ in there.

Therefore, $x+y$ is divisible by $2$ and is even.