Is the sum of two odd numbers always odd?

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Answer 1 · 2015-09-21T14:37:17

The sum of two odd numbers is always even.

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

If $n_1$ and $n_2$ are odd then $EE k_1, k_2$ such that $n_1 = 2k_1 + 1$ and $n_2 = 2k_2 + 1$ .

So we find:

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

which is a multiple of $2$ and therefore even.

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