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Re: Xmas puzzle

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  • Ralph Twain
    ... at X=59448^1801 ... has the (monic, ... the real part of ... I don t know much about number fields, so I can t say that it isn t relevant. Winding things
    Message 1 of 3 , Dec 30, 2005
      mikeoakes2@... wrote:
      ><ratwain@...> writes:
      >
      >>154275005845*59448^14408-3488484120*59448^12607+90930840*59448^10806+9177840*59448^9005-82990*59448^7204+16680*59448^5403+1
      >
      >This is the value of the polynomial
      >P(X)=154275005845*X^8-3488484120*X^7+90930840*X^6+9177840*X^5-82990*X^4+16680*X^3+1;
      at X=59448^1801
      >
      >According to PariGP, the number field defined by P(X)
      has the (monic,
      >simpler, irreducible) defining polynomial:
      >p(X)=x^8-4*x^7+77*x^6-217*x^5+1750*x^4-3143*x^3+12692*x^2-11156*x+23281
      >
      >And the polynomial p(X) has 4 pairs of complex roots,
      the real part of
      >each being [amazingly enough] precisely 1/2.
      >
      >Is this relevant, I wonder...?

      I don't know much about number fields, so I can't say
      that it isn't relevant.

      Winding things up in time for the new year: the
      answer I had in mind is that of Lucas primes.

      R.A. Twain




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