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23840Re: Primes again [really Mordell's equation]

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  • djbroadhurst
    Nov 30, 2011
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      --- In primenumbers@yahoogroups.com,
      "John" <mistermac39@...> wrote:

      > > No integral point Q on E(-27*k) results
      > > from a rational point P on E(k)
      >
      > I suspect this means there is no mapping, and one to one
      > or any other correspondences

      There are fancy names like injection and surjection
      that I tend to get the wrong way round. I think the
      right way round is to say that the map is injective,
      but not surjective.

      My heathen way of putting it is to say that every Q is mapped to
      by at most one P. But there are lots of Q's that are mapped to
      by no P's. And in the present case those Q's not given by P's
      include all the integral points that form Mike's data.
      At first I found this rather annoying. But then I realized that
      it provides a wonderful blind check, whose validity is widely
      believed, but not yet proven at the million-dollar mark.

      David
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