I am sorry for the bad title but I really can't think of a better one. So I was learning about the euclidean algorithm and I see a statement that is hard for me to understand. In the book that I was reading, it says that if X and Y are coprime integers, then (X-Y) and Y are also coprime. It says that this is really easy to prove, so the proof is omitted. Can anyone explain or write down the proof for this?