Multiplicative functions additive on polygonal numbers

Byungchan Kim; Ji Young Kim; Chong Gyu Lee; Poo Sung Park

doi:10.1007/s00010-021-00824-8

Multiplicative functions additive on polygonal numbers

Byungchan Kim, Ji Young Kim, Chong Gyu Lee, Poo Sung Park

School of Natural Sciences

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We prove that the set P (H, resp.) of all positive pentagonal (hexagonal, resp.) numbers is an additive uniqueness set for the collection of multiplicative functions; if a multiplicative function f satisfies the equation f(a+b)=f(a)+f(b)for all a, b∈ P (H, resp.), then f is the identity function.

Original language	English
Pages (from-to)	601-621
Number of pages	21
Journal	Aequationes Mathematicae
Volume	95
Issue number	4
DOIs	https://doi.org/10.1007/s00010-021-00824-8
State	Published - Aug 2021

Keywords

Additive uniqueness set
Functional equation
Hexagonal numbers
Multiplicative function
Pentagonal numbers
Polygonal numbers

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10.1007/s00010-021-00824-8

Cite this

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abstract = "We prove that the set P (H, resp.) of all positive pentagonal (hexagonal, resp.) numbers is an additive uniqueness set for the collection of multiplicative functions; if a multiplicative function f satisfies the equation f(a+b)=f(a)+f(b)for all a, b∈ P (H, resp.), then f is the identity function.",

keywords = "Additive uniqueness set, Functional equation, Hexagonal numbers, Multiplicative function, Pentagonal numbers, Polygonal numbers",

author = "Byungchan Kim and Kim, \{Ji Young\} and Lee, \{Chong Gyu\} and Park, \{Poo Sung\}",

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AU - Kim, Ji Young

AU - Lee, Chong Gyu

AU - Park, Poo Sung

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N2 - We prove that the set P (H, resp.) of all positive pentagonal (hexagonal, resp.) numbers is an additive uniqueness set for the collection of multiplicative functions; if a multiplicative function f satisfies the equation f(a+b)=f(a)+f(b)for all a, b∈ P (H, resp.), then f is the identity function.

AB - We prove that the set P (H, resp.) of all positive pentagonal (hexagonal, resp.) numbers is an additive uniqueness set for the collection of multiplicative functions; if a multiplicative function f satisfies the equation f(a+b)=f(a)+f(b)for all a, b∈ P (H, resp.), then f is the identity function.

KW - Additive uniqueness set

KW - Functional equation

KW - Hexagonal numbers

KW - Multiplicative function

KW - Pentagonal numbers

KW - Polygonal numbers

UR - https://www.scopus.com/pages/publications/85111771293

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JF - Aequationes Mathematicae

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ER -

Multiplicative functions additive on polygonal numbers

Abstract

Keywords

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