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Description of interesting failed factor algorithm

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  • Kermit Rose
    To factor the arbitrary positive integer z, I found integers h1, h2, h3,h4 such that h1 + h2 + h3 + h4 = z and h1 * h4 - h2 * h3 = 0. Then I expected that x =
    Message 1 of 1 , Oct 4, 2008
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      To factor the arbitrary positive integer z,

      I found integers

      h1, h2, h3,h4 such that

      h1 + h2 + h3 + h4 = z
      and

      h1 * h4 - h2 * h3 = 0.

      Then I expected that x = gcd(h1,h2) + gcd(h3,h4) would divided z.

      Indeed, x does divide z.

      x seems to always be equal to 1.

      I haven't yet found a way to generate a set h1,h2,h3,h4
      such that all of them are positive,
      and
      h1 + h2 + h3 + h4 = z,
      and
      h1 h4 - h2 h3 = 0.


      Kermit
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