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My question again

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  • Hugo Scolnik (fiber)
    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
    Message 1 of 4 , Nov 1, 2005
      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]
    • 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 2 of 4 , Nov 1, 2005
        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 3 of 4 , Nov 1, 2005
          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 4 of 4 , Nov 1, 2005
            > 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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