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:

>

> Dear all:

>

> 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..

>

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

quadratic

> 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]

>