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Re: Prime chains x-->Ax+B [puzzle 2]

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  • djbroadhurst
    ... Many congratulations, from UK and Estonia! David
    Message 1 of 143 , Jan 5, 2011
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      --- In primenumbers@yahoogroups.com,
      Kevin Acres <research@...> wrote:

      > So, after ~30 15/16 chains I can now post:
      >
      > [18, -143835631, [44253593, 16]]
      >
      > [1, 44253593, Mat([44253593, 1])]
      > [2, 652729043, Mat([652729043, 1])]
      > [3, 11605287143, Mat([11605287143, 1])]
      > [4, 208751332943, Mat([208751332943, 1])]
      > [5, 3757380157343, Mat([3757380157343, 1])]
      > [6, 67632698996543, Mat([67632698996543, 1])]
      > [7, 1217388438102143, Mat([1217388438102143, 1])]
      > [8, 21912991742002943, Mat([21912991742002943, 1])]
      > [9, 394433851212217343, Mat([394433851212217343, 1])]
      > [10, 7099809321676076543, Mat([7099809321676076543, 1])]
      > [11, 127796567790025542143, Mat([127796567790025542143, 1])]
      > [12, 2300338220220315922943, Mat([2300338220220315922943, 1])]
      > [13, 41406087963965542777343, Mat([41406087963965542777343, 1])]
      > [14, 745309583351379626156543, Mat([745309583351379626156543, 1])]
      > [15, 13415572500324833126982143, Mat([13415572500324833126982143, 1])]
      > [16, 241480305005846996141842943, Mat([241480305005846996141842943, 1])]
      > [17, 4346645490105245930409337343, [17, 1; 29, 1; 2092457, 1;
      > 4213575300261521443, 1]]

      Many congratulations, from UK and Estonia!

      David
    • djbroadhurst
      ... Suppose that we want to start with a square and get a square. Then we must solve the Diophantine equation y^2 = a*x^2 + b For any pair (a,b), Dario will
      Message 143 of 143 , Jan 7, 2011
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        --- In primenumbers@yahoogroups.com,
        Kevin Acres <research@...> wrote:

        > x=a*x+b either is a square or has a square as a major factor.

        Suppose that we want to start with a square and get a square.
        Then we must solve the Diophantine equation
        y^2 = a*x^2 + b

        For any pair (a,b), Dario will tell us all the solutions:
        http://www.alpertron.com.ar/QUAD.HTM

        David
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