## Re: My question again

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• The paper located at xxx.arXiv.org/physics/0503159 answers your question. Regards, Gordon physics/0503159 [abs, ps, pdf, other] : Title: Fast Factoring of
Message 1 of 4 , Nov 1 12:01 PM
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The paper located at xxx.arXiv.org/physics/0503159 answers

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
original analysis
Subj-class: General Physics

--- In primenumbers@yahoogroups.com, "Hugo Scolnik \(fiber\)"
<scolnik@f...> wrote:
>
> Dear all:
>
> I have posted the question appearing below and there was no single
>
> 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..
>
> 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, 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
Message 2 of 4 , Nov 1 12:13 PM
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Tuesday, November 01, 2005 8:40 PM [GMT+1=CET],
Hugo Scolnik (fiber) <scolnik@...> escribió:

> Dear all:
>
> I have posted the question appearing below and there was no single
>
> 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..
>

Hugo,

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@...
• ... 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
Message 3 of 4 , Nov 1 1:53 PM
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> I have posted the question appearing below and there was no single