  In this note, we characterize all functions $f : \mathbb{N} \rightarrow
\mathbb{C}$ such that $f(x_1^2+ \cdots + x_k^2)=f(x_1)^2+ \cdots + f(x_k)^2$,
where $k \geq 3$ and $x_1, \cdots, x_k$ are positive integers.
