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correction to CONTEST++

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  • 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 1 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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