I have a formula F that takes an ordered pair (a,b) of positive integer variables and outputs an unique positive integer c for each pair. Then I was working around with the formula and noticed that where i is added to a and subtracted from b to get (a',b') and in every case F(a',b') equals c + i . Then I thought that since i is both added and subtracted, the sum of the pair does not change with the value i and you can make i equal a+b-c so that F(a',b') = a' + b'. This gave the following ordered pairs for each integer: . . . -4 (6,-10) -3 (3,-6) -2 (1,-3) -1 (0,-1) 0 (0, 0) 1 (1, 0) 2 (3, -1) 3 (6, -3) Here a and b are the positive and negative triangular numbers. The ordered pairs form a curve. In between points could be filled in by making a and b real instead of integers. Now if i is added to each a and subtracted from each b the shape of the curve does not change. What is the formula for such a curve that passes through the above points? Please help me.