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Re: Interesting page for the number crunchers

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  • djbroadhurst
    Thanks for an interesting pointer, Jon. They key point is Faltings proof (1983) of the Mordell conjecture: there are only finitely many rational points on any
    Message 1 of 1 , Jun 1, 2002
      Thanks for an interesting pointer, Jon.

      They key point is Faltings' proof (1983)
      of the Mordell conjecture:
      there are only finitely
      many rational points on any
      curve of genus greater than one.

      So hunting for *integer* solutions to
      (x^n-1)/(x-1)=y^2 for n>3
      beyond the obvious
      (x,n,y)=(7,4,20),(3,5,11)
      is likely to be *very* unrewarding.
      I do not recommend that folk spend
      cycles on it. If you do, take
      n>5, since Elkies must have
      thrashed n=4,5 close to death.

      David
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