Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2021; 58(3): 603-608

Online first article February 22, 2021      Printed May 31, 2021

https://doi.org/10.4134/BKMS.b200399

Copyright © The Korean Mathematical Society.

Multiplicative functions which are additive on triangular numbers

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

Supported by: This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Science and ICT(NRF-2017R1A2B1010761)