## correction to CONTEST++

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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
Message 1 of 2 , Dec 22 10:24 AM
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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