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correction to CONTEST++

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  • aldrich617
    A , A + 1*B*10 , A + 4*B*10 + 60, A + 9*B*10 + 360, S + 16* B*10 + 1200� should read: A^2, A^2 + 1*B*10 , A^2 + 4*B*10 + 60, A^2 + 9*B*10 + 360, A^2 + 16* B*10
    Message 1 of 2 , Dec 22, 2007
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      A , A + 1*B*10 , A + 4*B*10 + 60,
      A + 9*B*10 + 360, S + 16* B*10 + 1200…

      should read:

      A^2, A^2 + 1*B*10 , A^2 + 4*B*10 + 60,
      A^2 + 9*B*10 + 360, A^2 + 16* B*10 + 1200…

      Aldrich
    • aldrich617
      I felt that I needed to clarify another point in the second question. So here I will post the restated CONTEST++ in its entirety: I offer a $51 prize to the
      Message 2 of 2 , Dec 22, 2007
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        I felt that I needed to clarify another point
        in the second question. So here I will post
        the restated CONTEST++ in its entirety:

        I offer a $51 prize to the first person who can submit
        a verifiable counterexample by New Year's day
        either for the following conjectures.

        (x,A,B,c,k,f : integers)
        Let A = 20x^2 + 10x + 1;
        Let B = 10x^2 + 4x + 1;
        Let c = trunc(A/sqrt(5)) - 1;

        1) For any x > 0, apply the issquare test to each k
        in the interval c <= k < B.
        If there exists a value of k that satisfies the
        conditions of the test, then A is composite,
        and there will be at least one value of k such
        that 2*k - 1 will have a factor in A.
        (issquare test: 0 < 5*(2*k -1)^2 - 4*A^2 = f^2)

        2) For any x > 0, if A and B are placed in the formula
        below, the five values can be used to make a polynomial
        or a set of difference equations that will generate a
        fourth degree sequence.

        A^2 , A^2 + 1*B*10 , A^ + 4*B*10 + 60,
        A^2 + 9*B*10 + 360, A^2 + 16* B*10 + 1200…

        The result will always be either a pure +1 mod 10 sequence
        (all prime factors end in one) or a defective +1 mod 10
        sequence (all prime factors end in one, except for a
        finite number of distinct squares of primes that end in
        nine occurring at regular intervals):

        As I really want these questions settled, I would be happy
        to assist any interested person.

        Aldrich
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