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 $k=2$.
Keywords : additive uniqueness, multiplicative function, triangular numbers
MSC numbers : 11P32, 11A25
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