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25186Re: Pell Equation

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  • djbroadhurst
    Jun 23, 2013
      --- In primenumbers@yahoogroups.com,
      Kermit Rose <kermit@...> wrote:

      > if
      > a1^2 - d b1^2 = 1
      > a2^2 - d b2^2 = 1
      > then
      > (a1^2 + d b1^2)^2 - (2 d a1 b1)^2 = 1
      > (a1 a2 + d b1 b2)^2 - d (a1 b2 + b1 a2)^2 = 1

      Indeed. Yet it is both clearer and more efficient to
      take powers of a unit. I illustrated this for positive
      d=4 mod 3, where one takes uses quadunit(4*d),
      with positive norm. The extension to other
      discriminants is straightforward. Moreover
      "quadunit" yields the building block that Kermit
      assumed to have been found, by undisclosed methods :-)

      David
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