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Sunday, November 05, 2017

How can you know? Social problem.

Reality can be so uncaring can seem cruel. And have noted a bizarre situation with number theory where is SO easy to know am correct, but how do you handle the emotions?

For instance, there is one key equation in an important way I solve for a generalized quadratic factorization:

g1(x) = f1(x)/k

Where that k messes so many things up. If k = 1 or -1, then you have number theory as was known. But if you choose to let be some other integers, then you know something is wrong.

The full factorization is in the complex plane:

P(x) = (g1(x) + 1)(g2(x) + 2)

where P(x) is a primitive quadratic with integer coefficients, g1(0) = g2(0) = 0, but g1(x) does not equal 0 for all x.

The other substitution is: g2(x) = f2(x) + k-2

Multiply both sides by k, and substitute for the g's, which gives me the now symmetrical form:

k*P(x) =  (f1(x) + k)(f2(x) + k)

The purpose is forcing symmetry. So the f's can be forced to be algebraic integers. But here is what is difficult for the emotions, they STILL can be so forced, when k is say, 2 or 3, and then you are forced that one of the g's cannot be when P(x) is irreducible.

That full post is here.

Easy algebra but HUGE consequences that rock number theory for over a hundred years all the way back to the late 1800's. And why would you bother to believe? If the truth hurts?

Hence what I call, the social problem. Is where emotion has taken over reason in math community, and yes, I DO understand. Is so hard. And the math does not care.


James Harris

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