## JSH: Leverage in the construction

The secret to the power of the seemingly simple construction I use is as easy as 1, 2, 3:

9(g_1(x) + 1)(g_2(x) + 2) = (f_1(x) + 9)(f_2(x) + 9) = 9*P(x)

where g_1(0) = g_2(0) = 0, one of the f's equals 0, at x=0, and P(x) is a quadratic with integer coefficients.

The leverage I use here is that multiplying times 1 or 2 is trivial. So it actually IS trivial to see how the 9 multiplies, as 9(1) = 9, but 9(2) = 18.

Years ago I called it a balance I think. I'm chaining the functions to easy constants—1 and 2—so that I can force them to behave in a particular way, by the distributive property.

The result is so powerful that you may notice that no actual mathematician has stepped up, even in Usenet posts, to dispute it, and posters who argue with me, have not been established mathematicians!!!

There is no way to dispute the result mathematically. It just is a mathematical fact that what you multiply times an expression will show up, if you multiply 1 or 2. So if it's x, you get 2x, if you multiply times 2. If it's pi, you get 2*pi.

And by the distributive property:

a*(f(x) + b) = a*f(x) + a*b

The triviality of the proof has been there for over seven years, as in, it's easy. I've yet to find a mathematician, an actual professional mathematician, who has disputed it. As how can they? And I welcome any to step up in reply to this post to tell me they are ready to jump in line and dispute the result.

So it's easy to prove 9, or previously I used 7, as a factor in those cases I give all the time in various threads. And the idea of unit factors not units in the ring of algebraic integers is not rocket science, so mathematicians would trivially comprehend it.

The secret is in the construction, forcing the functions across from integers, which is why forcing values at x=0 is so important. In trying to dispute the distributive property, various posters have been very creative in coming up with bizarre "functions", but those are just attempts at disputing the distributive property, as:

a*(f(x) + b) = a*f(x) + a*b

does not distinguish between f(0) and other values. So their "functions" are attempts at refuting the distributive property, which of course sounds ludicrous, so they claim they aren't!!!

Why then would mathematicians not just acknowledge my research?

Good question. Best guess is that they prefer the error!!!

Most of them were brought up in it. It was around before they were born.

It's like a religion. It's the religion they learned.

They live in error because error is what is now natural to them.

It's correct mathematics which may seem strange to a professional mathematician who has known only error his entire life—but believed otherwise, until a powerful, but simple mathematical construction was like a physicist telling a devout Fundamentalist Christian that Jesus didn't walk on water.