Comptes Rendus
no. 2
Number theory
Multiplicative functions additive on generalized pentagonal numbers

Presented by: the Editorial Board

Byungchan Kim1; Ji Young Kim2; Chong Gyu Lee3; Poo-Sung Park4
1 School of Liberal Arts, Seoul National University of Science and Technology, 232 Gongneung-ro, Nowon-gu, Seoul 01811, Republic of Korea
2 Department of Mathematical Sciences, Seoul National University, 1 Gwanak-ro, Gwanak-Gu, Seoul 08826, Republic of Korea
3 Department of Mathematics, Soongsil University, 369 Sangdo-ro, Dongjak-gu, Seoul 06978, Republic of Korea
4 Department of Mathematics Education, Kyungnam University, Changwon-si, Gyeongsangnam-do 51767, Republic of Korea
Comptes Rendus. Mathématique, Volume 356 (2018) no. 2, pp. 125-128.

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.

Nous prouvons que l'ensemble GP de tous les nombres pentagonaux généralisés non nuls est un ensemble d'unicité additive ; si une fonction multiplicative f satisfait l'équation

f(a+b)=f(a)+f(b),
pour tous a,b∈GP, alors f est la fonction identité.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2017.12.011

Byungchan Kim 1; Ji Young Kim 2; Chong Gyu Lee 3; Poo-Sung Park 4

1 School of Liberal Arts, Seoul National University of Science and Technology, 232 Gongneung-ro, Nowon-gu, Seoul 01811, Republic of Korea
2 Department of Mathematical Sciences, Seoul National University, 1 Gwanak-ro, Gwanak-Gu, Seoul 08826, Republic of Korea
3 Department of Mathematics, Soongsil University, 369 Sangdo-ro, Dongjak-gu, Seoul 06978, Republic of Korea
4 Department of Mathematics Education, Kyungnam University, Changwon-si, Gyeongsangnam-do 51767, Republic of Korea 
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Byungchan Kim; Ji Young Kim; Chong Gyu Lee; Poo-Sung Park. Multiplicative functions additive on generalized pentagonal numbers. Comptes Rendus. Mathématique, Volume 356 (2018) no. 2, pp. 125-128. doi : 10.1016/j.crma.2017.12.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.12.011/

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