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November 3rd, 2008, 10:07 PM   #1
duz
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A Diophantine equation

Please find a non-zero integer solution for equation
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November 5th, 2008, 06:54 PM   #2
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Re: A Diophantine equation

(1, -1, -2, -2, -2, 4 - sqrt(2))
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November 5th, 2008, 11:09 PM   #3
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Re: A Diophantine equation

Quote:
Originally Posted by CRGreathouse
(1, -1, -2, -2, -2, 4 - sqrt(2))
4- is not integer
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November 6th, 2008, 04:39 AM   #4
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Re: A Diophantine equation

Ah, missed that, sorry. I wasn't able to find any nonzero integer solutions.
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November 6th, 2008, 04:43 AM   #5
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Re: A Diophantine equation

Mathematica 6.0 fails:
Code:
In[1]:= FindInstance[
 a^2 + b^2 + c^2 + d^2 + e^2 + f^2 == a b c d e f && a > 0, {a, b, c, 
  d, e, f}, Integers]

During evaluation of In[1]:= FindInstance::nsmet: The methods \
available to FindInstance are insufficient to find the requested \
instances or prove they do not exist. >>

Out[1]= FindInstance[
 a^2 + b^2 + c^2 + d^2 + e^2 + f^2 == a b c d e f && a > 0, {a, b, c, 
  d, e, f}, Integers]
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November 6th, 2008, 04:07 PM   #6
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Re: A Diophantine equation

Hehe, How if there're 5 or 7 variables instead of 6 variables?
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November 7th, 2008, 11:17 AM   #7
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Re: A Diophantine equation

It's can't find anything for 5. For 7, it gives (3, 2, 2, 2, 1, 1, 1).
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November 7th, 2008, 02:25 PM   #8
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Re: A Diophantine equation

So it seems it is not so good.
For five numbers, below is a solution
1 1 3 3 4
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November 7th, 2008, 02:29 PM   #9
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Re: A Diophantine equation

In fact, I have proved that there're no non-zero solutions for 6 variables with help of computer:
See more details at http://zdu.spaces.live.com/blog/cns!...2037!164.entry
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