## JSH: Just math

Given z^2 = y^2 + T

where T is composite, and y and z are coprime integers, for any factorizations of T into two positive integers f_1 and f_2, where there exists an odd prime p less than both, or if f_1 is the smaller factor p-f_1 is less than f_1, where also exists an alpha such that

k^2 = (1 + alpha^2)^{-1}(T) mod p

then

z = (1 + 2alpha^2)k/(2alpha).

That is just math. It is absolutely perfect math, but it is just math.

The politics though are bigger than mathematical proof when it comes to acceptance.

I remember last year when I had that result, kind of vaguely though as to know when I had it I do searches in Google Groups and they indicate December 2007. It seemed so neat. Just this beautiful little result.

It's a deeper number theoretic structure underlying a familiar equation.

Maybe you thought you knew

z^2 = y^2 + T

but you didn't. With integers there is that deeper structure. I call it the z constraint.

A big deal if number theorists were real researchers, but they're fakes.

I now have all these nice research results. So many I forget what I have, as if it matters.