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.