Eugene Salamin wrote:

Is there a similar formula for the number r3(n) of integer solutions (x,y,z) of

x^2 + y^2 + z^2 = n ?

Davenport in The Higher Arithmetic says (end of chapter V, after discussing two and four squares) "The number of representations by three squares is a much more recondite function, but can be expressed in terms of certain class numbers of quadratic forms." Looking in Dickson's History of the Theory of Numbers, vol 3, p.109: if 12E(n) is the number of representations of n as a sum of three squares, then E(n) = 2F(n) - G(n) where G(n) = number of classes of determinant -n F(n) = number of uneven classes [of determinant -n ?] This is due to Kronecker. Class here means equivalence class of binary quadratic forms, I presume. I don't know what an "uneven" class is. There may be some constants omitted here. Gary McGuire