Quantum Gravity 194.0: Additive Monochromatic Decomposition of Polynomials
- From: OsherD <mdoctorow@xxxxxxxxx>
- Date: Tue, 30 Oct 2007 12:08:01 -0700
From Osher Doctorow
Hongze Li and Hao Pan, arXiv: 0710.5344 v1 [math.NT] 29 Oct 2007, 13
pages, in "Two addition theorems on polynomials of prime variables,"
prove a fascinating theorem on monochromatic decomposition of
polynomials w(x) with integral coefficients and positive leading
coefficient (one other condition is stated below), the decomposition
being of form:
1) w(z) = x + y
where x and y are monochromatic in coloring of all positive integers
with m colors, x does not equal y, and z is in LAMBDA_bo, Wo defined
by:
2) LAMBDA_b, W = {x: Wx + b is prime}
where m, bo, Wo are positive integers such that bo < = Wo, (bo, Wo) =
1, and:
3) w(1) o w(0) is even if 2 | Wo (Wo is divisible by 2)
4) w(bo - 1) is even if Wo is not divisible by 2.
Li and Pan are from Shanghai Jiaotong U. China.
Although they don't research from the viewpoint of Probable Causation/
Influence (PI), the additive decompositions of polynomials (especially
simple decompositions like this into only two x and y) give an
additional fundamental importance to PI main operations of addition
and subtraction.
Osher Doctorow
.
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