1. The problem statement, all variables and given/known data Well, the problem is a discrete math problem to prove that the difference of an even integer and an odd integer is an odd integer. 2. Relevant equations If you let m = an even integer, and n = an odd integer then m = 2r for some integer r, while n = 2s + 1 for some integer s. 3. The attempt at a solution Then m - n = 2r - (2s + 1) = 2r - 2s - 1 at the next step, the answer in the book shows 2(r-s-1)+1, from there I can follow the rest of the steps to show that an integer is odd but I'm confused as to where this extra one is coming from. I know it's just a basic factoring question, but I'm a little rusty, maybe somebody could help me.. thanks.