My Math Forum Express a cube as sum of squares ....

 Number Theory Number Theory Math Forum

August 29th, 2013, 03:57 PM   #11
Member

Joined: Apr 2013

Posts: 70
Thanks: 0

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

Quote:
 Originally Posted by CRGreathouse If you're allowed unbounded sums there are thousands of identities. You can check this one with Faulhaber's formula, if you like.
There is no link to Faulhaber's formula.

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:
Originally Posted by icemanfan
Quote:
 Originally Posted by Mouhaha Sorry. Im talking about a general formula. n^3 is expressed by ns (squares and degree 1)
There is no formula in terms of a quadratic function that would work for all n. This is what I meant when I said the only way to represent $n^3$ in terms of n is $n^3$.
Look at my way to write n^3

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:
Originally Posted by Mouhaha
Quote:
 Originally Posted by CRGreathouse If you're allowed unbounded sums there are thousands of identities. You can check this one with Faulhaber's formula, if you like.
There is no link to Faulhaber's formula.

It is about combinatorials not sum of powers
You're summing a quadratic. If you can't see the link between that and Faulhaber's formula, then it wouldn't help if I explained it.

 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 k-1) +3n^2-2n When is n is odd =2k+1 n^3=6*(sigma((2i+1)^2) with i=0 to k-1) +3n^2-2n 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:
 Originally Posted by Mouhaha Can you rewrite my formulas in Latex? It would help a lot I think.
For n even:

$n^3= 6\sum_{i=1}^{n-1} 2i^2 + 3n^2 - 2n$

For n odd:

$n^3= 6\sum_{i=0}^{n-1}(2i+1)^2 + 3n^2 - 2n$

 Tags cube, express, squares, sum

,
,

,

,

,

,

,

,

,

# express cube maths

Click on a term to search for related topics.
 Thread Tools Display Modes Linear 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