What 2 odd numbers added together equal an odd number?

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Answer 1 · 2015-09-08T22:53:10

Let say you have the odd number #a=2*k+1# and another odd #b=2m+1# if you add them you get

#a+b=2(k+m)+2=2(k+m+1)# which is even.

Answer 2 · 2015-09-08T23:13:36

In normal integer arithmetic the sum of two odd numbers will always be even and not odd.

In modulo arithmetic with an odd base all numbers are both odd and even, so any two numbers work.

For example, in modulo #5# arithmetic, #3+3 = 1#, which are obviously all odd numbers.

Less obviously, in modulo #3# arithmetic #1+1=2# is an example, since #2 = 2*2 + 1#