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August 31st, 2013, 12:51 PM  #31  
Member Joined: Apr 2013 Posts: 70 Thanks: 0  Re: Express a cube as sum of squares .... Quote:
 
August 31st, 2013, 06:10 PM  #32  
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:
 
September 3rd, 2014, 11:34 AM  #33 
Newbie Joined: Sep 2014 From: Seattle Posts: 1 Thanks: 0 Math Focus: Number theory 
"You can express any nonnegative integer as a sum of four squares. " This seems incorrect. Certainly said integer would have to be at least 4, but I can't fathom any four squares that add to 5, 6, 8, 9... I think I could go on. 
September 3rd, 2014, 11:45 AM  #34  
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  Quote:
If you want numbers that are the sum of four nonzero squares you're looking for https://oeis.org/A000414 rather than the nonnegative integers.  
September 3rd, 2014, 03:23 PM  #35  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408  Hello, Mouhaha! Quote:
I assume you mean a sum of distinct squares. Otherwise, we have these trivial solutions: $\qquad \begin{array}{ccc}2^3 &=& 2^2+2^2 \\ 3^3 &=& 3^2+3^2+3^2 \\ 4^3 &=& 4^2+4^2+4^2+4^2 \\ \vdots && \vdots \end{array}$  

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