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24108Re: Two large consecutive smooth numbers

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  • Jim White
    Mar 4, 2012
       
      Hi kermit,
       
      The quadratic case simply corresponds to a 3-tuple
      of smooth {Q, Q+1, Q+2} inferring a pair at
      {(Q+1)^2 - 1, (Q+1)^2}
       
      We are aiming for more massive "power boosting".
       
      cf: Prouhet-Tarry-Escott problem.
       
      Warrens SMODA II document has a good list of
      known cases for polynomials to orders up to 10,
      and I believe he has found pairs using a 12-th degree
      poly.
       
      Cheers!


      ________________________________
      From: Kermit Rose <kermit@...>
      To: primenumbers@yahoogroups.com
      Sent: Monday, 5 March 2012, 1:59
      Subject: [PrimeNumbers] Re: Two large consecutive smooth numbers

      > I will guess that maybe the only quadratic polynomial solutions are
      > translations of the first example.

      Cubic polynomial solutions should be more prolific.

      Kermit




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