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From: Osher Doctorow on 1 Aug 2010 01:44
From Osher Doctorow

Repulsion is not simply a concept in physics, but in mathematical
Number Theory, and two U.K. researchers at U. East Anglia Norwich
U.K., Graham Everest and Thomas Ward, in:

1) "The repulsion motiv in Diophantine equations," arXiv: 1005.0315
v3[math.NT] 27 May 2010, 17 pages

advance the theory of integral powers repulsion and also repulsion by
or from the "point at infinity" (look up the latter on Wikipedia or
Wolfram, relating to complex variable analysis).

For example, Siegel's Theorem says that:

1) y^2 = x^3 + d

has only finitely many integral solutions (for y and x) given a
nonzero integer d. This can be interpreted to say that the point at
infinite repels integer points on the curve of (1), that is, there is
a neighborhood (possibly punctured) of the point at infinity that has
no integer points.

Repulsion of this type is often indicated by inequalities on absolute
values:

2) |y^2 - x^3| > C(log x)^(10)^(-4) for some constant C = C(x) for x,
y positive integers such that y^2 does not equal x^3 (a result of
Baker)

3) |y^2 - x^3| > C(log x)^k for every k < 1, for some constant C =
C(x). This is a result of Stark.

The integers repel each other in this sense, not just are repelled by
the point at infinity.

Osher Doctorow

From: John on 1 Aug 2010 23:38

"Osher Doctorow" <osherdoctorow87(a)gmail.com> wrote in message
news:36ad699a-a7be-453e-9c99-c007c02a9b28(a)i18g2000pro.googlegroups.com...
> From Osher Doctorow
>
> Repulsion is not simply a concept in physics, but in mathematical
> Number Theory, and two U.K. researchers at U. East Anglia Norwich
> U.K., Graham Everest and Thomas Ward, in:
>
> 1) "The repulsion motiv in Diophantine equations," arXiv: 1005.0315
> v3[math.NT] 27 May 2010, 17 pages
>
> advance the theory of integral powers repulsion and also repulsion by
> or from the "point at infinity" (look up the latter on Wikipedia or
> Wolfram, relating to complex variable analysis).
>
> For example, Siegel's Theorem says that:
>
> 1) y^2 = x^3 + d
>
> has only finitely many integral solutions (for y and x) given a
> nonzero integer d. This can be interpreted to say that the point at
> infinite repels integer points on the curve of (1), that is, there is
> a neighborhood (possibly punctured) of the point at infinity that has
> no integer points.
>
> Repulsion of this type is often indicated by inequalities on absolute
> values:
>
> 2) |y^2 - x^3| > C(log x)^(10)^(-4) for some constant C = C(x) for x,
> y positive integers such that y^2 does not equal x^3 (a result of
> Baker)
>
> 3) |y^2 - x^3| > C(log x)^k for every k < 1, for some constant C =
> C(x). This is a result of Stark.
>
> The integers repel each other in this sense, not just are repelled by
> the point at infinity.
>
> Osher Doctorow
>

repel = dipshit
Repulsion = a post by kOsher Duckanspew


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