- The paper located at xxx.arXiv.org/physics/0503159 answers

your question.

Regards,

Gordon

physics/0503159 [abs, ps, pdf, other] :

Title: Fast Factoring of Integers

Authors: Gordon Chalmers

Comments: 8 pages, LaTeX, v1: correction to a_{C_N}\neq 1 and

improved analysis to general case, v2: added addendum paper to

original analysis

Subj-class: General Physics

--- In primenumbers@yahoogroups.com, "Hugo Scolnik \(fiber\)"

<scolnik@f...> wrote:>

answer.

> Dear all:

>

> I have posted the question appearing below and there was no single

>

attention to the irrelevant.

> Best

>

> Hugo Scolnik

>

> A programming language is low level when its programs require

>

------------------------------------------------------------------

> -------------------------------------------------------------------

> I am interested in knowing proven results regarding the

possibility of

> generating perfect squares with expressions like

expression

> a + bt

>

> 1) it is obvious that not always is possible to get squares. E.g.

>

> a = 281941 = 11*19*19*71

>

> b = 510510 = 2*3*5*7*11*13*17

>

>

> because a + b*t = 11*(25631 + 46410*t) and therefore if the

> between parentheses does not give an odd power of 11..

quadratic

>

> 2) when a +bt generates squares, t can be written as a number of

> polynomials. How many ? The number depends on

> the factorization of b ?

>

> Hope somebody can provide answers

>

> Thank you

>

> Hugo Scolnik

>

> [Non-text portions of this message have been removed]

> - Tuesday, November 01, 2005 8:40 PM [GMT+1=CET],

Hugo Scolnik (fiber) <scolnik@...> escribió:

> Dear all:

Hugo,

>

> I have posted the question appearing below and there was no single

> answer.

>

> Best

>

> Hugo Scolnik

>

> A programming language is low level when its programs require

> attention to the irrelevant.

>

> -------------------------------------------------------------------------------------------------------------------------------------

> I am interested in knowing proven results regarding the possibility of

> generating perfect squares with expressions like

> a + bt

>

> 1) it is obvious that not always is possible to get squares. E.g.

>

> a = 281941 = 11*19*19*71

>

> b = 510510 = 2*3*5*7*11*13*17

>

>

> because a + b*t = 11*(25631 + 46410*t) and therefore if the expression

> between parentheses does not give an odd power of 11..

>

If t = 0 (mod 11), a + b*t can't be multiple of 11, but in other case yes.

By example, for t = 10,

a + 10*b = 11*(25631 + 46410*10) = 11*489731 = 11*(11*211^2) = (11*211)^2

In generall, for t = 10 (mod 11), a + b*t = 0 (mod 11^2)

Best regards,

Ignacio Larrosa Cañestro

A Coruña (España)

ilarrosa@... > I have posted the question appearing below and there was no single

answer.

Dear Hugo,

Please see message 17083, where I explained why your satement about

"no squares" was wrong, gave a generic formula for generating an

infinite number of squares of the form, and pointed you to a web

reference that could be used to generate several other infinite series

of squares of the form, and a tutorial section to explain how the

infinite solutions were generated.