August 29th, 2013, 03:57 PM  #11  
Member Joined: Apr 2013 Posts: 70 Thanks: 0  Re: Express a cube as sum of squares .... Quote:
It is about combinatorials not sum of powers  
August 29th, 2013, 04:00 PM  #12  
Member Joined: Apr 2013 Posts: 70 Thanks: 0  Re: Express a cube as sum of squares .... Quote:
 
August 29th, 2013, 04:13 PM  #13  
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:
 
August 29th, 2013, 04:14 PM  #14 
Member Joined: Apr 2013 Posts: 70 Thanks: 0  Re: Express a cube as sum of squares ....
When n is even =2k n^3 = 6*(sigma(2i^2) with i=1 to k1) +3n^22n When is n is odd =2k+1 n^3=6*(sigma((2i+1)^2) with i=0 to k1) +3n^22n In Latex it will be great. (Edited and corrected) 
August 29th, 2013, 04:19 PM  #15 
Member Joined: Apr 2013 Posts: 70 Thanks: 0  Re: Express a cube as sum of squares ....
Can you rewrite my formulas in Latex? It would help a lot I think. 
August 29th, 2013, 04:23 PM  #16 
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 ....
Maybe you should grab gp (link in my .sig) and use sumformal() to prove them. (You could also use the WZ method, as found in the free (!) book A = B, but that would take much longer to learn!)

August 29th, 2013, 04:28 PM  #17 
Member Joined: Apr 2013 Posts: 70 Thanks: 0  Re: Express a cube as sum of squares ....
1^2+2^2+3^2+4^2+.....n^2 which is the purpose Faulhaber`s formula is different from what I proposed 1^2+2^2+3^2+4^2+.....n^2 can be expressed as sum of 2 combinatorials C(a,3)+C(b,3) 
August 29th, 2013, 04:30 PM  #18 
Member Joined: Apr 2013 Posts: 70 Thanks: 0  Re: Express a cube as sum of squares ....
Did you get that there is something new in my formulas? If you did not then .............. 
August 29th, 2013, 04:47 PM  #19 
Member Joined: Apr 2013 Posts: 70 Thanks: 0  Re: Express a cube as sum of squares ....
1^2+2^2+3^2+4^2+.....n^2 can be expressed as sum of 2 factorials C(a,3)+C(b,3) For example : 1^2+2^2+3^2+4^2+.....11^2= C(12,3)+C(13,3) General formula for n 1^2+2^2+3^2+4^2+.....n^2=C(n+1,3)+C(n+2,3) 
August 29th, 2013, 05:35 PM  #20  
Senior Member Joined: Feb 2012 Posts: 628 Thanks: 1  Re: Express a cube as sum of squares .... Quote:
For n odd:  

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