>>7624352An odd number can be written as 2k + 1 where k is an integer.
The sum of three arbitrary odd numbers, 2m + 1, 2n + 1, and 2j + 1, will be
(2m + 1) + (2n + 1) + (2j + 1)
= 2m + 2n + 2j + 3
= 2(m + n + j + 1) + 1
(m + n + j + 1) is an integer because the set of integers is closed under addition.
Therefore, the sum of any 3 odd integers is odd.
But yeah if you redefine the system as base-(some odd number), it will work because that turns some of the listed numbers into even numbers. As in
>>7624464 
