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Author: galathaeagalathaea Date: Oct 4, 2007 22:32
for positive inputs
(a - z^2 - x - 1)^2 + ((z + 1)^2 - a - y - 1)^2 = 0
this is the diophantine intersection at a value of
D(a, x, y, z) := (a - z^2 - x - 1)^2 + ((z + 1)^2 - a - y - 1)^2
to transform it to allow the entire integral domain
it becomes
D(a_0^2 + a_1^2 + a_2^2 + a_3^2 + 1,
x_0^2 + x_1^2 + x_2^2 + x_3^2 + 1,
y_0^2 + y_1^2 + y_2^2 + y_3^2 + 1,
z_0^2 + z_1^2 + z_2^2 + z_3^2 + 1)
and i use the modified putnam-adler polynomial
P_D = a(1 - D^2) - (t^2 + u^2 + v^2 + w^2)D^2
whose range should be deny(n^2)
including all negative integers
in other words
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Author: magpiesmnmagpiesmn Date: Oct 4, 2007 22:46
Love ya'z didnt totaly get the math but the poem was awsome.
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Author: galathaeagalathaea Date: Oct 5, 2007 00:32
On Oct 4, 10:32 pm, galathaea gmail.com> wrote:>
>
> for positive inputs
> (a - z^2 - x - 1)^2 + ((z + 1)^2 - a - y - 1)^2 = 0
>
> this is the diophantine intersection at a value of
>
> D(a, x, y, z) := (a - z^2 - x - 1)^2 + ((z + 1)^2 - a - y - 1)^2
>
> to transform it to allow the entire integral domain
> it becomes
>
> D(a_0^2 + a_1^2 + a_2^2 + a_3^2 + 1,
> x_0^2 + x_1^2 + x_2^2 + x_3^2 + 1,
> y_0^2 + y_1^2 + y_2^2 + y_3^2 + 1,
> z_0^2 + z_1^2 + z_2^2 + z_3^2 + 1)
>
> and i use the modified putnam-adler polynomial
> ...
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Date: Oct 5, 2007 21:26
On Oct 5, 6:17 am, quasi wrote:
>
> But how about version (2) of tommy1729's problem?
>
> Can you get a range of N\S?
There is a polynomial P which is always positive, and whose range is
precisely the positive integers which are not square. The proof is
short, an explicit construction. The "Matijasevic" theorem plays no
part.
I do not know whether I have erased what should be erased, nor do I
know whether this will appear in the middle like it is not supposed
to.
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Author: quasiquasi Date: Oct 5, 2007 21:59
On Fri, 05 Oct 2007 21:26:55 -0700, adler.math@ gmail.com wrote:
>On Oct 5, 6:17 am, quasi wrote:
>>
>> But how about version (2) of tommy1729's problem?
>>
>> Can you get a range of N\S?
>
>There is a polynomial P which is always positive, and whose range is
>precisely the positive integers which are not square. The proof is
>short, an explicit construction. The "Matijasevic" theorem plays no
>part.
Let's see it.
>I do not know whether I have erased what should be erased, nor do I
>know whether this will appear in the middle like it is not supposed
>to.
Your posting style looks fine now.
quasi
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Author: quasiquasi Date: Oct 5, 2007 22:04
On Sat, 06 Oct 2007 00:59:05 -0400, quasi wrote:
>On Fri, 05 Oct 2007 21:26:55 -0700, adler.math@ gmail.com wrote:
> >>On Oct 5, 6:17 am, quasi wrote:
>>>
>>> But how about version (2) of tommy1729's problem?
>>>
>>> Can you get a range of N\S?
>>
>>There is a polynomial P which is always positive, and whose range is
>>precisely the positive integers which are not square. The proof is
>>short, an explicit construction. The "Matijasevic" theorem plays no
>>part.
>
>Let's see it.
Let me guess ...
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Date: Oct 5, 2007 22:09
On Oct 5, 9:26 pm, adler.m...@ gmail.com wrote: > On Oct 5, 6:17 am, quasi wrote:
>> But how about version (2) of tommy1729's problem?
>
>> Can you get a range of N\S?
I think there is something I am not seeing. The range is the positive
non-squares, {2, 3, 5, 6, 7, 8, 10, ....}. Is that not what was being
looked for? The polynomial is never negative, indeed never 0.
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Author: quasiquasi Date: Oct 5, 2007 22:13
On Fri, 05 Oct 2007 22:09:30 -0700, adler.math@ gmail.com wrote:
>On Oct 5, 9:26 pm, adler.m...@ gmail.com wrote: >> On Oct 5, 6:17 am, quasi wrote:
>>> But how about version (2) of tommy1729's problem?
>>
>>> Can you get a range of N\S?
>
>
>I think there is something I am not seeing. The range is the positive
>non-squares, {2, 3, 5, 6, 7, 8, 10, ....}. Is that not what was being
>looked for? The polynomial is never negative, indeed never 0.
I see a set, and it's the correct set.
But where's the polynomial?
We're talking _full_ ranges here, not just positive ranges.
quasi
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