Jun 272012
theorem Let \(n\) be a positive integer, then \(n\) can be expressed as the sum of three squares iff it is not of the form
\begin{equation}4^a(8b+7)\end{equation}
for some \( a,b\in\Bbb Z,a,b\geq 0\).
For a integer \(n\equiv3\pmod8\), there exists three odd numbers \(x,y,z\) such that
\begin{equation}n=x^2+y^2+z^2.\end{equation}