Are there any two odd numbers that equal an odd number?
I’ll assume that you are asking “Are there any two odd numbers whose SUM is equal to an odd number?” Recall that odd numbers are of the form 2n + 1 where n is an integer. Even numbers are of the form 2n where n is an integer. Suppose the sum of two odd numbers is an even number. Let the first odd number equal 2n + 1 and let the second odd number equal 2m + 1. Their sum is written as follows: (2n + 1) + (2m + 1) = 2m + 2n + 1 + 1 = 2(m + n) + 2 = 2[(m + n) + 1] Since (m + n) + 1 is again an integer, we can let k = (m + n) + 1. Therefore, (2n + 1) + (2m + 1) = 2k. Since 2k is an even integer, this contradicts our assumption that the sum of two odd numbers is odd. No, there are no two odd numbers whose sum is equal to an odd number. [Update] Sorry, Joy, you submitted your answer while I was typing. I didn’t see your answer until after I submitted mine.
