Multiplicative functions which are additive on triangular numbers
Bull. Korean Math. Soc. 2021 Vol. 58, No. 3, 603-608
https://doi.org/10.4134/BKMS.b200399
Published online February 22, 2021
Printed May 31, 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
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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