Multiplicative functions additive on generalized pentagonal numbers

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

doi:10.1016/j.crma.2017.12.011

Multiplicative functions additive on generalized pentagonal numbers

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

School of Natural Sciences

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

7 Scopus citations

Abstract

We prove that the set GP of all nonzero generalized pentagonal numbers is an additive uniqueness set; if a multiplicative function f satisfies the equation f(a+b)=f(a)+f(b), for all a,b∈GP, then f is the identity function.

Original language	English
Pages (from-to)	125-128
Number of pages	4
Journal	Comptes Rendus Mathematique
Volume	356
Issue number	2
DOIs	https://doi.org/10.1016/j.crma.2017.12.011
State	Published - Feb 2018

Access to Document

10.1016/j.crma.2017.12.011

Cite this

@article{fd6857e3f1ec4dd6bfbea16ff56116ec,

title = "Multiplicative functions additive on generalized pentagonal numbers",

abstract = "We prove that the set GP of all nonzero generalized pentagonal numbers is an additive uniqueness set; if a multiplicative function f satisfies the equation f(a+b)=f(a)+f(b), for all a,b∈GP, then f is the identity function.",

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

note = "Publisher Copyright: {\textcopyright} 2018 Acad{\'e}mie des sciences",

year = "2018",

month = feb,

doi = "10.1016/j.crma.2017.12.011",

language = "English",

volume = "356",

pages = "125--128",

journal = "Comptes Rendus Mathematique",

issn = "1631-073X",

number = "2",

}

TY - JOUR

T1 - Multiplicative functions additive on generalized pentagonal numbers

AU - Kim, Byungchan

AU - Kim, Ji Young

AU - Lee, Chong Gyu

AU - Park, Poo Sung

PY - 2018/2

Y1 - 2018/2

N2 - We prove that the set GP of all nonzero generalized pentagonal numbers is an additive uniqueness set; if a multiplicative function f satisfies the equation f(a+b)=f(a)+f(b), for all a,b∈GP, then f is the identity function.

AB - We prove that the set GP of all nonzero generalized pentagonal numbers is an additive uniqueness set; if a multiplicative function f satisfies the equation f(a+b)=f(a)+f(b), for all a,b∈GP, then f is the identity function.

UR - http://www.scopus.com/inward/record.url?scp=85040103151&partnerID=8YFLogxK

U2 - 10.1016/j.crma.2017.12.011

DO - 10.1016/j.crma.2017.12.011

M3 - Article

AN - SCOPUS:85040103151

SN - 1631-073X

VL - 356

SP - 125

EP - 128

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

IS - 2

ER -

Multiplicative functions additive on generalized pentagonal numbers

Abstract

Access to Document

Other files and links

Fingerprint

Cite this