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CONTEST++ two more conjectures, more $$

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  • aldrich617
    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 :
    Message 1 of 1 , Dec 21, 2007
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      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, then 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 , A + 1*B*10 , A + 4*B*10 + 60,
      A + 9*B*10 + 360, S + 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 those
      containing a finite number of squares of primes that
      end in nine):

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

      Aldrich Stevens
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