sum-difference number. Yet with the proof we just gave, we know that 6(2002) is also a sumdifference number, without having to use guess-and-check.
The goal throughout the rest of the paper is to characterize all sum-difference numbers. In order to accomplish this characterization, we need to establish the following list of facts: 1. Show that x is the largest of the four numbers x, y, w, & z. 2. Show that x/d = w/e. We will call this number a. 3. Show that z/d=y/e. Similarly, we call this number b. 4. Show that a and b are relatively prime and that a > b. 5. Show that (a – b)z = (a + b)y.
While showing these facts, we suppose n = xy = wz and x – y = w + z. We now begin by proving the facts in the above list.