That doesn't help, and I wonder if it's because I didn't explain my question well enough. Suppose I have a number N and I want to try using the "Difference of

That doesn't help, and I wonder if it's because I didn't explain my question well enough. Suppose I have a number N and I want to try using the "Difference of Rectangles" method to factor it. So I want to find integers a, b, and c that satisfy this: (a+c)a-(b+c)b=N I'm going to assume that, as with standard Fermat factoring, I will choose values for a and c, compute (a+c)a-N, and then try to solve for b. If I succeed then I'm done. But how do I choose my initial values of a and c? And if I then can't solve for b, how do I choose my next values of a and c? I don't need visualisations, I know the algebra and can form my own pictures of what's going on. I need to know how the algorithm chooses a and c, and then how it proceeds when b doesn't exist.