## 24380Re: Impossible to Prove ??

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• Aug 11, 2012
--- In primenumbers@yahoogroups.com, James Merickel <moralforce120@...> wrote:
>
> I think that having gone through (at least) 5 editions and been scrutinized by all of the best number theorists in the world for the better part of a century makes this a safe assumption.
> JGMÂ
>

Chapter 15 of Hardy/Wright looks to me like the basis
for the issquare functions. Can the appropriate issquare
for A = 14x^2 + 14xy + y^2 be expressed as 7(2x + y)^2 = 2A?

To get back to the original conjectures, I don't see how
it immediately follows from Hardy/Wright Theorem 257 that
A = 5x^2 + 5xy + y^2 has as values ALL of the possible
values of primes that are +/- 1 mod 10 while the similar
B = 5x^2 + 25xy + y^2 will not.

I also don't see how it immediately follows that
A = 2x^2 + 2xy + y^2 has as values ALL of the
possible values of primes that are +1 mod 4
while the similar B = 8x^2 + 8xy + y^2 will not.

Surely there must be more to the proofs than just
reading the definitions found in chapter 15.

Aldrich
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