User Name Remember Me? Password

 Number Theory Number Theory Math Forum

 August 29th, 2013, 05:53 PM #21 Global Moderator   Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms 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? August 29th, 2013, 10:56 PM   #22
Math Team

Joined: Mar 2012
From: India, West Bengal

Posts: 3,871
Thanks: 86

Math Focus: Number Theory
Re: Express a cube as sum of squares ....

Quote:
Originally Posted by icemanfan
Quote:
 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. August 30th, 2013, 12:41 AM   #23
Senior Member

Joined: Mar 2012
From: Belgium

Posts: 654
Thanks: 11

Re: Express a cube as sum of squares ....

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 August 30th, 2013, 04:19 AM   #24
Member

Joined: Apr 2013

Posts: 70
Thanks: 0

Re: Express a cube as sum of squares ....

Quote:
 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 August 30th, 2013, 04:22 AM #25 Member   Joined: Apr 2013 Posts: 70 Thanks: 0 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. August 30th, 2013, 04:24 AM   #26
Member

Joined: Apr 2013

Posts: 70
Thanks: 0

Re: Express a cube as sum of squares ....

Quote:
Originally Posted by icemanfan
Quote:
 Originally Posted by Mouhaha 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 August 30th, 2013, 04:26 AM #27 Member   Joined: Apr 2013 Posts: 70 Thanks: 0 Re: Express a cube as sum of squares .... So nothing new. The formula seems to be known. Is it useful? August 30th, 2013, 04:36 AM #28 Member   Joined: Apr 2013 Posts: 70 Thanks: 0 Re: Express a cube as sum of squares .... Sorry!!!!!!!!!!!!!! Sum up to 2(k-1) not n-1 August 30th, 2013, 10:25 AM   #29
Global Moderator

Joined: Nov 2006
From: UTC -5

Posts: 16,046
Thanks: 938

Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms
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. August 30th, 2013, 10:26 AM   #30
Global Moderator

Joined: Nov 2006
From: UTC -5

Posts: 16,046
Thanks: 938

Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms
Re: Express a cube as sum of squares ....

Quote:
 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. Tags cube, express, squares, sum ,
,

,

,

,

,

,

,

,

express cube maths

Click on a term to search for related topics.
 Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post king.oslo Algebra 3 September 6th, 2013 12:09 PM yano Algebra 8 March 25th, 2010 05:40 PM squidgy_wiji Advanced Statistics 8 August 17th, 2009 10:36 PM symmetry Algebra 4 June 3rd, 2007 12:57 PM yano Applied Math 4 December 31st, 1969 04:00 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top      