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.
Poo-Sung Park
Kyungnam University
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)
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