# Is the sum of two odd numbers always odd?

##### 1 Answer

Sep 21, 2015

#### Answer:

The sum of two odd numbers is always even.

It can only be odd (too) if using modular arithmetic with an odd modulus.

#### Explanation:

If

So we find:

#n_1 + n_2 = (2k_1 + 1) + (2k_2 + 1) = 2 (k_1 + k_2 + 1)#

which is a multiple of

In modular arithmetic with an odd modulus all numbers are both odd and even.