Much of what I have is challenging, in many ways. And even for me that can be daunting which is why like to have those results where can look at with nothing controversial.
One of my most important results follows from a generalized quadratic factorization but while there are important posts which cover everything, one of my recent favorites just focuses on the basic facts. For me can be comforting and will copy from it and link to it.
So yeah seen in LOTS of posts are some important things.
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 simplest example is: P(x) = x2 + 3x + 2
Introduce k, where k is a nonzero, and new functions f1(x), and f2(x), where:
g1(x) = f1(x)/k and 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)
Reference post: Simple generalized quadratic factorization
That post has nothing controversial. Is just a matter-of-fact stepping through a way to solve for the g's by solving for the f's using a rather simple technique. And I will at times just go over it.
Can feel weird how simply absolute mathematics can be. You have just these facts and logical connections to get to a conclusion, which is truth. And it just is. Like 2+2=4, like to say to myself.
Look at things now, over and over again, and just wonder. Is weird for it to feel weird. But sometimes, yeah, say to myself, I found that. And eventually, move away, think about other things.
The results are there for me whenever I need them. Whenever I want to wonder.
Which can also be shared for those who want that as well. Is just knowledge.
James Harris
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