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Old 2007-10-26, 18:38   #1
kpatsak
 
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Default Representation of integer as sum of squares

Is there a formula that gives the number of representations of n as a sum four squares? Any help would be more than appreciated.
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Old 2007-10-27, 09:22   #2
cheesehead
 
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"Richard B. Woods"
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If you haven't already seen it, let me introduce you to The On-Line Encyclopedia of Integer Sequences (OEIS) at http://www.research.att.com/~njas/sequences/. (If you have seen it, did you know you could use its search function on words, not just numbers?) Try OEIS search on "sum four squares".

Last fiddled with by cheesehead on 2007-10-27 at 09:25
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Old 2007-10-27, 10:26   #3
kpatsak
 
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Default The encyclopedia

I have seen this encyclopedia, moreover I have searched it.
It doesn't contain the sequence that I want and for many of the sequences it does not contain it's formula
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Old 2007-10-27, 22:10   #4
R. Gerbicz
 
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"Robert Gerbicz"
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Quote:
Originally Posted by kpatsak View Post
Is there a formula that gives the number of representations of n as a sum four squares? Any help would be more than appreciated.
It's well known: f[n]=8*sum((d|n)&&(d%4>0),d)
See:
http://mathworld.wolfram.com/SumofSquaresFunction.html
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Old 2007-10-29, 17:53   #5
cheesehead
 
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Quote:
Originally Posted by kpatsak View Post
I have seen this encyclopedia, moreover I have searched it.
It doesn't contain the sequence that I want and for many of the sequences it does not contain it's formula
When I searched OEIS on "sum four squares" the second page of returned results included

http://www.research.att.com/~njas/sequences/A000118 "Number of ways of writing n as a sum of 4 squares"

which looks like "number of representations of n as a sum four squares". Among the several given formulas seems (to me) to be one equivalent to what R. Gerbicz quoted above.

If A000118 (1,8,24,32,24,48,96,64,24,104,144,96,96,112,...) isn't what you want, can you list a few specific values of what you seek?

Last fiddled with by cheesehead on 2007-10-29 at 18:26 Reason: Quoted terms from A000118
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