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Re: Interesting page for the number crunchers

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  • 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 1 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 2 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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