Is every positive integer the sum of two distinct positive odd integers?

Is every positive integer the sum of two distinct positive odd integers?
No. You can't derive 2 or any odd number from the sum of 2 positive odd integers. You can't get 2 because you would be forced to add 1 with 1. Which isn't distinct, and you can't get an odd number at all since both the other numbers are odd. Say the first one is of the form 2n+1 and the second is 2m+1. (2n+1)+(2m+1)=2n+2m+2=2(m+n+1) which has to be even.