no. 2
Number theory
Multiplicative functions additive on generalized pentagonal numbers
[Les fonctions multiplicatives qui sont additives sur les nombres pentagonaux généralisés]

Présenté par : the Editorial Board

Kim, Byungchan1 ; Kim, Ji Young2 ; Lee, Chong Gyu3 ; Park, Poo-Sung4
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, Tome 356 (2018) no. 2, pp. 125-128.

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.

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.

Reçu le :
Accepté le :
Publié le :
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 
@article{CRMATH_2018__356_2_125_0,
     author = {Kim, Byungchan and Kim, Ji Young and Lee, Chong Gyu and Park, Poo-Sung},
     title = {Multiplicative functions additive on generalized pentagonal numbers},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {125--128},
     publisher = {Elsevier},
     volume = {356},
     number = {2},
     year = {2018},
     doi = {10.1016/j.crma.2017.12.011},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2017.12.011/}
}
TY  - JOUR
AU  - Kim, Byungchan
AU  - Kim, Ji Young
AU  - Lee, Chong Gyu
AU  - Park, Poo-Sung
TI  - Multiplicative functions additive on generalized pentagonal numbers
JO  - Comptes Rendus. Mathématique
PY  - 2018
SP  - 125
EP  - 128
VL  - 356
IS  - 2
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2017.12.011/
DO  - 10.1016/j.crma.2017.12.011
LA  - en
ID  - CRMATH_2018__356_2_125_0
ER  - 
%0 Journal Article
%A Kim, Byungchan
%A Kim, Ji Young
%A Lee, Chong Gyu
%A Park, Poo-Sung
%T Multiplicative functions additive on generalized pentagonal numbers
%J Comptes Rendus. Mathématique
%D 2018
%P 125-128
%V 356
%N 2
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2017.12.011/
%R 10.1016/j.crma.2017.12.011
%G en
%F CRMATH_2018__356_2_125_0
Kim, Byungchan; Kim, Ji Young; Lee, Chong Gyu; Park, Poo-Sung. Multiplicative functions additive on generalized pentagonal numbers. Comptes Rendus. Mathématique, Tome 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/

[1] Bašić, B. Characterization of arithmetic functions that preserve the sum-of-squares operation, Acta Math. Sin., Volume 30 (2014), pp. 689-695

[2] Chung, P.V. Multiplicative functions satisfying the equation f(m2+n2)=f(m2)+f(n2), Math. Slovaca, Volume 46 (1996), pp. 165-171

[3] Chung, P.V.; Phong, B.M. Additive uniqueness sets for multiplicative functions, Publ. Math. (Debr.), Volume 55 (1999), pp. 237-243

[4] Dubickas, A.; Šarka, P. On multiplicative functions which are additive on sums of primes, Aequ. Math., Volume 86 (2013), pp. 81-89

[5] Fang, J.-H. A characterization of the identity function with equation f(p+q+r)=f(p)+f(q)+f(r), Combinatorica, Volume 31 (2011), pp. 697-701

[6] Park, P.-S. Multiplicative functions commutable with sums of squares, Int. J. Number Theory (2018) (in press) | DOI

[7] Park, P.-S. On k-additive uniqueness of the set of squares for multiplicative functions, Aequ. Math. (2018) (in press) | DOI

[8] Park, P.-S. On multiplicative functions which are additive on almost primes, Publ. Math. (Debr.) (2018) (in press)

[9] Spiro, C.A. Additive uniqueness sets for arithmetic functions, J. Number Theory, Volume 42 (1992), pp. 232-246

Cité par Sources :