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Another example of Matrix Factor Elements and Addition table

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  • Kermit Rose
    The fundamental Matrix Factor Elements are; [0, 3, 6, 9, 14, 16, 17, 18, 19] The addition table is: 0 2 4 6 8 10 11 2 4 6 8 10 12 13 5
    Message 1 of 2 , Dec 16, 2006
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      The fundamental Matrix Factor Elements are;
      [0, 3, 6, 9, 14, 16, 17, 18, 19]


      The addition table is:

      0 2 4 6 8 10 11
      2 4 6 8 10 12 13
      5 7 9 11 13 15 16
      8 10 12 14 16 18 19


      The equivalent Matrix Factor Element sets displayed in a way to show
      their equivalence.

      0 2 2 4 4 5 6 6 7 8 8 8 9 10 11 12 13 10 10 11 12 13 14 15 16 16 18 19
      0 3 6 9 14
      16 17 18 19


      Notice that the addition table has the elements almost but not quite in
      numerical order by reading along the reverse diagonals.

      Does anyone have any hints for more quickly finding the equivalent
      Matrix Factor Element set that can be arranged into an
      addition table?


      Kermit < kermit@... >
    • Phil Carmody
      ... So it s a set { a_{i,j} : a_{i,j} = a_{1,j} + a_{i,1} if i 1 or j 1 } In that case, the whole thing becomes trivial. Sum { 2^{a_{i,1}} } * Sum {
      Message 2 of 2 , Dec 17, 2006
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        --- Kermit Rose <kermit@...> wrote:
        > The fundamental Matrix Factor Elements are;
        > [0, 3, 6, 9, 14, 16, 17, 18, 19]
        >
        > The addition table is:
        >
        > 0 2 4 6 8 10 11
        > 2 4 6 8 10 12 13
        > 5 7 9 11 13 15 16
        > 8 10 12 14 16 18 19

        So it's a set { a_{i,j} : a_{i,j} = a_{1,j} + a_{i,1} if i>1 or j>1 }

        In that case, the whole thing becomes trivial.

        Sum { 2^{a_{i,1}} } * Sum { 2^{a_{1,j}} } = N

        So if N is prime, no such representation exists.

        Phil

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