Multiplicative functions which are additive on triangular numbers
Bull. Korean Math. Soc. Published online February 22, 2021
Poo-Sung Park
Kyungnam University
Abstract : Fix $k \ge 3$. If a multiplicative function $f$ satisfies
\[
f(x_1+x_2+\dots+x_k) = f(x_1) + f(x_2) + \dots + f(x_k)
\]
for arbitrary positive triangular numbers $x_1, x_2, \dots, x_k$, then $f$ is the identity function. This extends Chung and Phong's work for $k=2$.
