Could the (z) be singling out the z. What could z mean? Riemann Zeta function? N just sideways in our end record?
Also Fermat factorization method is just testing squares out to see if its a difference of them right? Basically the equivalent of doing the F function (incrementing d) repeatedly until e is a square. Then if e is a square (say of radius r) then you would satisfy the equation:
c = d^2 - r^2 which would imply that c = (d+r)(d-r)
This would mean that a = d-r, b = d+r, e = r^2
Also the pi thing is basically the amount of iterations it takes to go greater than 2 while just outside the cups of the mandelbrot set approaches pi to an increasing power. Looks like a cornucopia.