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Re: some questions about algebraic factoring in the field of adjoined square

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  • djbroadhurst
    ... In the case of positive d = 3 mod 4, used quadunit(4*d), in Pari-GP, and then take powers of this unit, which has norm = +1. Here is an example with d =
    Message 1 of 2 , Jun 21, 2013
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      --- In primenumbers@yahoogroups.com,
      "bhelmes_1" <bhelmes@...> asked:

      > d=4n+2 or d=4n+3
      > and the equation of Pell a^2-d*b^2=1
      > What is the fastest way to solve the equation of Pell

      In the case of positive d = 3 mod 4,
      used quadunit(4*d), in Pari-GP,
      and then take powers of this unit,
      which has norm = +1.

      Here is an example with d = 139:

      {d=139;q=quadunit(4*d);r=1;
      for(n=1,100,r*=q;print([n,a=real(r),b=imag(r)]))}

      [1, 77563250, 6578829]
      [2, 12032115501124999, 1020550716868500]
      [3, 1866499965285267079810250, 158314460780301358671171]
      ...

      NB: At n=100, "a" has 819 decimal digits.

      David
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