From: dredmond@math.siu.edu (Don Redmond)
Newsgroups: can.schoolnet.math.sr,sci.math,alt.math.undergrad,alt.uu.math.misc
Subject: Re: Math Problems
Date: 12 Jan 1997 00:09:29 GMT

In article <5b929j$8kj@opus.vcn.bc.ca>, landmark@vcn.bc.ca (Scott Phung) wrote:

--
> 
> My second question is:
> 
> Given the equation x^2 + y^2 + z^2 = n,
> 
> with x, y, z being integers and n a positive integer,
> 
> how many different solutions (x,y,z) are there?
> 
> (ie (0,1,2), (0,-1,2),(-1,2,0), and (-2,0,1) are
> all different solutions and are counted seperately).
> 
> (This is just like Jacobi's Four-Square Theorem but with
> three squares).
> 
Check E. Grosswald's book on Representations by Squares.
(This is not the correct title, but should be close enough.)
He gives the counting function for sums of three squares.
It is not anywhere as neat as sums of two or four squares.
Don