20 Nov
2002
20 Nov
'02
1:21 p.m.
There is a nice way to calculate the number r2(n), n>0, of integer solutions (x,y) of x^2 + y^2 = n. Factor n as n = p1^a1 p2^a2 ... q1^b1 q2^b2 ... 2^c, where the p's are primes == 1 mod 4, and the q's are primes == 3 mod 4. Then r2(n) = if any b is odd, then 0 else, 4 (1 + a1) (1 + a2) ... . Is there a similar formula for the number r3(n) of integer solutions (x,y,z) of x^2 + y^2 + z^2 = n ? __________________________________________________ Do you Yahoo!? Yahoo! Web Hosting - Let the expert host your site http://webhosting.yahoo.com