Round 1: Problem 5

Begin with a set of distinct positive integers. A new positive integer may be constructed and added to the set so long as it has the form (a+b)/(a-b) where a and b are already in the set. (For example, if 9 and 6 are already in the set, then the number 5 may be added.) The original set of integers is called “prolific” if every positive integer can eventually be constructed and added to the set. What is the smallest size that a prolific set can have? Prove your answer.