Arithmetic functions commutable with sums of squares

Jungin Lee

In this note, we characterize all functions $f:\mathbb{N}\to \mathbb{C}$ such that $f(x_1^2+\cdots +x_k^2)=f(x_1{)}^2+\cdots +f(x_k{)}^2$, where $k\ge 3$ and $x_1, \cd…