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Re: [PrimeNumbers] Re: Prime chains x-->Ax+B [puzzle 2]

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  • Kevin Acres
    Hello David, ... Something like [18*x-448552937, [15788701, 15]] probably violates your search criteria. I just need to know if A
    Message 1 of 143 , Jan 4, 2011
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      Hello David,

      At 07:31 AM 20/11/2010, djbroadhurst wrote:

      >Please read the rules for the bounded case:
      >http://tech.groups.yahoo.com/group/primenumbers/message/22087
      >
      > > Let A, B and L be integers with A > 1 and L > 1.
      > >
      > > Definition: A "Smith chain" of length L is a chain
      > > p[n+1] = A*p[n] + B, such that p[n] is prime,
      > > for n = 1 to L, with p[2] > p[1] > A.
      >
      > > Definition: A "maximal Smith chain" is a Smith chain with
      > > integers (A,B) for which there is a proof that no chain
      > > of greater length exists.

      Something like [18*x-448552937, [15788701, 15]] probably violates
      your search criteria.

      I just need to know if A < p[1] < p[2] can be stretched to A <
      abs(p[1]) < abs(p[2]) or is that outside of these rules?


      Best Regards,

      Kevin. (with 25 conforming 15/16s)
    • djbroadhurst
      ... Suppose that we want to start with a square and get a square. Then we must solve the Diophantine equation y^2 = a*x^2 + b For any pair (a,b), Dario will
      Message 143 of 143 , Jan 7, 2011
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        --- In primenumbers@yahoogroups.com,
        Kevin Acres <research@...> wrote:

        > x=a*x+b either is a square or has a square as a major factor.

        Suppose that we want to start with a square and get a square.
        Then we must solve the Diophantine equation
        y^2 = a*x^2 + b

        For any pair (a,b), Dario will tell us all the solutions:
        http://www.alpertron.com.ar/QUAD.HTM

        David
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