1. The problem statement, all variables and given/known data Let b be a positive integer and consider any set S of b+1 positive integers. Show that there exists two diﬀerent numbers x, y ∈ S so that x mod b = y mod b 2. Relevant equations 3. The attempt at a solution Pretty stumped. I tried for a while to use different values of b but I soon realized that this could lead to pretty much infinite amounts of any different positive integers in my set.