Is the sum of two odd numbers always odd?
The sum of two odd numbers is always even.
It can only be odd (too) if using modular arithmetic with an odd modulus.
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.