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Re: My question again

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  • gordon_as_number
    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, 2005
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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 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]
      >
    • Ignacio Larrosa Cañestro
      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, 2005
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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
        > 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..
        >

        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@...
      • elevensmooth
        ... 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, 2005
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          > 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.
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