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Interesting page for the number crunchers

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  • Jon Perry
    Namely, when is a repunit a square in a given base: http://www.mathematik.uni-bielefeld.de/~sillke/PROBLEMS/reputnic_squares Jon Perry perry@globalnet.co.uk
    Message 1 of 3 , Jun 1, 2002
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      Namely, when is a repunit a square in a given base:

      http://www.mathematik.uni-bielefeld.de/~sillke/PROBLEMS/reputnic_squares

      Jon Perry
      perry@...
      http://www.users.globalnet.co.uk/~perry/maths
      BrainBench MVP for HTML and JavaScript
      http://www.brainbench.com
    • djbroadhurst
      Standard Pellian analysis shows that (x^4-1)/(x-1)=y^2 has no integer solution for odd x in [9,10^20000] The probabilty of a solution with odd x 10^20000 is
      Message 2 of 3 , Jun 1, 2002
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        Standard Pellian analysis shows that
        (x^4-1)/(x-1)=y^2
        has no integer solution for
        odd x in [9,10^20000]

        The probabilty of a solution with
        odd x > 10^20000 is about
        1 part in 10^10000, so
        I wouldn't advise "number crunching" :-)

        David
      • Jon Perry
        Two points: 1) Does the Mordell conjecture still hold for y^n? 2) I think this is the law of small numbers, but how is the theorem that if an equation has no
        Message 3 of 3 , Jun 1, 2002
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          Two points:

          1) Does the Mordell conjecture still hold for y^n?

          2) I think this is the law of small numbers, but how is the theorem that if
          an equation has no solutions to some very large n, then it is true/false
          holding water.

          Jon Perry
          perry@...
          http://www.users.globalnet.co.uk/~perry/maths
          BrainBench MVP for HTML and JavaScript
          http://www.brainbench.com


          -----Original Message-----
          From: djbroadhurst [mailto:d.broadhurst@...]
          Sent: 01 June 2002 13:04
          To: primenumbers@yahoogroups.com
          Subject: [PrimeNumbers] Re: Interesting page for the number crunchers


          Standard Pellian analysis shows that
          (x^4-1)/(x-1)=y^2
          has no integer solution for
          odd x in [9,10^20000]

          The probabilty of a solution with
          odd x > 10^20000 is about
          1 part in 10^10000, so
          I wouldn't advise "number crunching" :-)

          David



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