Here's a tired thought off the top of my head that I've applied no context to: e and -f in n=1 are 2d+1 apart. This is equivalent to 2d(n-0) + nn from the (x+n)(x+n), since n=1. We're finding (e,1) and (-f,1) based on a set d, e and f value with an assumed n. So what if we instead assumed n=2, and we found (e,2) and (-f,2) and so on upwards? Would this relationship hold (2d(n-0) + nn gap between (e,2) and (-f,2))?