# What 2 odd numbers added together equal an odd number?

Let say you have the odd number $a = 2 \cdot k + 1$ and another odd $b = 2 m + 1$ if you add them you get

$a + b = 2 \left(k + m\right) + 2 = 2 \left(k + m + 1\right)$ which is even.

Sep 8, 2015

For example, in modulo $5$ arithmetic, $3 + 3 = 1$, which are obviously all odd numbers.
Less obviously, in modulo $3$ arithmetic $1 + 1 = 2$ is an example, since $2 = 2 \cdot 2 + 1$