Given n, find (x, y, z) with x^2 + y^2 + z^2 = n

Question

Can anyone tell me if there is a polynomial time algorithm which, given an integer n, returns all triples of integers whose squares sum to n?
Alternatively I could use an algorithm which enumerates the triples whose squares sum to 1, then to 2, etc.
thanks

Answer 1

The following (naive) algorithm does the job in O(n^1.5); is this what you had in mind?
public class xyz {
     public static void process(int x, int y, int z, int n) {
          System.out.println(n+": "+x+" "+y+" "+z);
     public static void f(int n) {
          for (int x= 0; x*x <= n; ++x)
               for (int y= 0; x*x+y*y <= n && y <= x; ++y) {
                    for (int z= 0; x*x+y*y+z*z <= n && z <= y; ++z)
                         if (x*x+y*y+z*z == n)
                              process(x, y, z, n);
     public static void main(String[] args) {
          for (int n= 0; n < 1000; ++n)
               f(n);
}kind regards,
Jos