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August 29th, 2013, 05:53 PM   #21
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Re: Express a cube as sum of squares ....

Both of those formulas, as written, are false. Perhaps you meant to sum up to something other than n-1?
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August 29th, 2013, 10:56 PM   #22
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Re: Express a cube as sum of squares ....

Quote:
Originally Posted by icemanfan
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Originally Posted by CRGreathouse
You can express any nonnegative integer as a sum of four squares.
Do you know how to prove that? I would be interested in seeing the argument.
That is Lagrange's four square theorem. It is a well-known special case of the Waring problem.
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August 30th, 2013, 12:41 AM   #23
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Re: Express a cube as sum of squares ....

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Originally Posted by CRGreathouse
(You could also use the WZ method, as found in the free (!) book A = B, but that would take much longer to learn!)
Is it this book ? http://www.math.upenn.edu/~wilf/AeqB.html
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August 30th, 2013, 04:19 AM   #24
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Re: Express a cube as sum of squares ....

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Originally Posted by CRGreathouse
Both of those formulas, as written, are false. Perhaps you meant to sum up to something other than n-1?
Right.
I mistaped n instead of k assuming that n even is equal to 2k and n odd =2k+1
So you sum up to 2(k-1).

Edited twice
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August 30th, 2013, 04:22 AM   #25
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Re: Express a cube as sum of squares ....

Correction 2

When n is even =2k

n^3 = 6*(sigma(2i^2) with i=1 to 2(k-1)) +3n^2-2n

When is n is odd =2k+1

n^3=6*(sigma((2i+1)^2) with i=0 to 2(k-1)) +3n^2-2n

In Latex it will be great.
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August 30th, 2013, 04:24 AM   #26
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Re: Express a cube as sum of squares ....

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Can you rewrite my formulas in Latex?
It would help a lot I think.
For n even=2k



For n odd=2k+1

Corrected twice
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August 30th, 2013, 04:26 AM   #27
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Re: Express a cube as sum of squares ....

So nothing new.
The formula seems to be known.
Is it useful?
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August 30th, 2013, 04:36 AM   #28
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Re: Express a cube as sum of squares ....

Sorry!!!!!!!!!!!!!!
Sum up to 2(k-1) not n-1
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August 30th, 2013, 10:25 AM   #29
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Re: Express a cube as sum of squares ....

Quote:
Originally Posted by gelatine1
Quote:
Originally Posted by CRGreathouse
(You could also use the WZ method, as found in the free (!) book A = B, but that would take much longer to learn!)
Is it this book ? http://www.math.upenn.edu/~wilf/AeqB.html
Yes. I highly recommend it.
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August 30th, 2013, 10:26 AM   #30
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Re: Express a cube as sum of squares ....

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Originally Posted by Mouhaha
So nothing new.
The formula seems to be known.
Is it useful?
I don't know of any applications for this particular formula, but there are certainly uses for the general method of turning the sum of a polynomial into a polynomial of higher degree.
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