Hoping to stay decent one day at a time
Big into recreational mathematics - Number theory, Factorization Algorithms, Primality testing.. I have tried to stay away from "classical" ideas that may have become hard to change over the years so that I can more easily develop an approach to problems on my own.
I am more of a critic now. As Kronecker said, God gave us the Integers... I'm not sure we need much else and I feel that most of mathematics today is too defined. I try my best to adhere to a constructionist mentality and I even rewrote the fundemental theorem of arithmetic for myself. That's what a constructionist does when something out there doesn't make enough sense.
I've recently written an algorithm that isolates the entire infinite field of prime numbers equal or greater than 3, and I'm proud to have gotten this far. It is loosely based on quadratic reciprocity. I don't feel that we should be describing composites solely by the composition of their prime factors when we have other ways to do it.
For each set of two factors of an integer N from 1 to infinity, there exists a set of squares who's difference is equal to the product of factors.
If a number only has itself and 1 as factors, it is said to be prime and will only be represented numerically be the difference of a single, unique set of squares A^2 and B^2, where A-B = 1
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