Number theory
Multiplicative functions additive on generalized pentagonal numbers
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.

Accepted:
Published online:
DOI: 10.1016/j.crma.2017.12.011
Kim, Byungchan 1; Kim, Ji Young 2; Lee, Chong Gyu 3; Park, Poo-Sung 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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Kim, Byungchan; Kim, Ji Young; Lee, Chong Gyu; Park, Poo-Sung. 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. http://www.numdam.org/articles/10.1016/j.crma.2017.12.011/

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