# how many natural numbers on a sphere

how many natural solutions are there to the following equation: $$\sum_{i=0}^k x_i^2 = n$$ where $n,k \in\ \Bbb{N}$
i well like to get a answer for every n and k, but could do with just $k=2,3$.

-
Have a look at math.stackexchange.com/questions/86178/… and the links there. –  Gerry Myerson Sep 21 '12 at 12:55
Also related: math.stackexchange.com/questions/88826/… –  Gerry Myerson Sep 21 '12 at 12:58
–  David Speyer Sep 21 '12 at 13:18