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Evolving factoring efforts

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  • Kermit Rose
    One of my factoring schemes evolved into the following. z represents the integer to be factored. Let r1,r2,r3 be three primes selected so that (r1 + r2 + r3 +
    Message 1 of 1 , May 4, 2008
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      One of my factoring schemes evolved into the following.

      z represents the integer to be factored.

      Let r1,r2,r3 be three primes selected so that

      (r1 + r2 + r3 + z) / 4 is an integer.


      Consider the equation

      ( 4 f2 + r2) * ( 4 f3 + r3) = (4 f1 + r1) z

      If we can solve this equation, we can expect that

      < for some solutions > that

      (4 f2 + r2) and (4 f3 + r3) have factors in common with z.



      The equation

      ( 4 f2 + r2) * ( 4 f3 + r3) = (4 f1 + r1) z

      Breaks into the six modulus equations

      (4 f2 + r2) = 4 p1 f1 z mod r1
      p1 ( 4 f3 + r3 ) = 4 f1 z mod r1

      4 f2 = p2 (4 f1 + r1) z mod r2
      p2 (4 f3 + r3) = (4 f1 + r1) z mod r2


      (4 f2 + r2) = p3 (4 f1 + r1) z mod r3
      4 p3 f3 = (4 f1 + r1) z mod r3



      Hopefully, we might be able to solve these 6 modulus equations
      for
      p1,p2,p3,f1,f2,f3,

      and then use them to determine values for the f1,f2,f3 in the equation


      ( 4 f2 + r2) * ( 4 f3 + r3) = (4 f1 + r1) z.





      Kermit Rose

      < kermit@... >
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