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19302Reducing factoring problem to linear equations

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  • Kermit Rose
    Mar 5, 2008
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      I blundered into a new approach to factoring.

      Given the positive integer z to be factored,

      find a matrix

      [A -B]
      [C D]

      which has determinant equal to Z.

      Then apply the general solution to


      [ a1 a2 ] [ b1 b2 ] = [ c1 * d1 c2 * d2 ]
      [ a3 a4 ] [ b3 b4 ] = [ c3 * d3 c4 * d4 ]

      to reduce the factoring of Z to the factoring of A, B, C, and D.

      I have hope that I've reduced the problem of finding the general solution to


      [ a1 a2 ] [ b1 b2 ] = [ c1 * d1 c2 * d2 ]
      [ a3 a4 ] [ b3 b4 ] = [ c3 * d3 c4 * d4 ]

      to the problem of solving 32 linear equations in 32 variables.


      Kermit Rose < kermit@... >