Proof

[Artur]

Dear Max,
In case that m isn't square x is irrational number (surely not positive 
integer)
Best wishes
Artur


Max Alekseyev pisze:
> On Wed, Apr 23, 2008 at 8:49 AM, Artur <grafix at csl.pl> wrote:
>   
>> Dear Neil,
>>  I hope that I have proof:
>>     
>
> Your proof works only in one direction. Namely, you have proved that
> if a prime is of the form 4 x^2 - 4 x*y + 7 y^2 then is is also of the
> form 24n + 7. To prove the converse, you need to prove the existence
> of a solution in the following sub-problem:
>
>   
>>  2) Now if we solve equation (7 k + 7 k^2 - x - 2 k x + x^2) = m on variable
>> x and we will be forced x as positive integer
>>  we are receiving
>>  x=(1+2k+/-Sqrt[-24k^2-24k+4m+1])/2
>>  now to integer x condition need     -24k^2-24k+4m+1 have to be odd square
>>     
>
> The question is WHY such a square EXISTS for a particular value of m?
> Maybe there exists such m that -24k^2-24k+4m+1 is never a square?
>
> Regards,
> Max
>
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