Geodesic
On relations associated with the Euler function
Diskretnyj analiz i issledovanie operacij, Tome 30 (2023) no. 4, pp. 35-45.

Voir la notice de l'article provenant de la source Math-Net.Ru

The paper studies the properties of the set of numbers smaller than and coprime to $n$ with the modulo $n$ multiplication operation introduced on it (this object is sometimes called the Euler group). The cardinality of such a set is the well-known Euler function $\varphi(n),$ which is one of the classical functions in the number theory. The fields of its application are quite wide and include, for example, various branches of discrete mathematics, and it also has significant applications in cryptography. The paper considers various combinatorial problems arising in the study of the Euler group and the Euler function. Relations between theoretical and numerical parameters associated with the Euler group and Euler function are derived. The combinatorial relations obtained in the paper can be used when solving applied combinatorial problems and in cryptography. Bibliogr. 10.
Keywords: divisor, Euler function, Stirling numbers, Möbius function, generating function.
Mots-clés : Euler group 
@article{DA_2023_30_4_a2,
     author = {V. K. Leontiev and E. N. Gordeev},
     title = {On relations associated with the {Euler} function},
     journal = {Diskretnyj analiz i issledovanie operacij},
     pages = {35--45},
     publisher = {mathdoc},
     volume = {30},
     number = {4},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2023_30_4_a2/}
}
TY  - JOUR
AU  - V. K. Leontiev
AU  - E. N. Gordeev
TI  - On relations associated with the Euler function
JO  - Diskretnyj analiz i issledovanie operacij
PY  - 2023
SP  - 35
EP  - 45
VL  - 30
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DA_2023_30_4_a2/
LA  - ru
ID  - DA_2023_30_4_a2
ER  - 
%0 Journal Article
%A V. K. Leontiev
%A E. N. Gordeev
%T On relations associated with the Euler function
%J Diskretnyj analiz i issledovanie operacij
%D 2023
%P 35-45
%V 30
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DA_2023_30_4_a2/
%G ru
%F DA_2023_30_4_a2
V. K. Leontiev; E. N. Gordeev. On relations associated with the Euler function. Diskretnyj analiz i issledovanie operacij, Tome 30 (2023) no. 4, pp. 35-45. http://geodesic.mathdoc.fr/item/DA_2023_30_4_a2/

[1] V. I. Arnold, Euler Groups and Arithmetics of Geometric Progression, MTsNMO, M., 2003 (Russian)

[2] V. N. Sachkov, An Introduction to Combinatorial Methods of Discrete Mathematics, MTsNMO, M., 2004 (Russian) | MR

[3] A. P. Alfyorov, A. Yu. Zubov, A. S. Kuzmin, A. V. Cheryomushkin, Basics of Cryptography, Gelios ARV, M., 2002 (Russian)

[4] R. L. Graham, D. E. Knuth, O. Patashnik, Concrete Mathematics: A Foundation for Computer Science, Addison-Wesley, Reading, MA, 1994 | MR | MR | Zbl

[5] Hardy G. H., Wright E. M., An introduction to the theory of numbers, Clarendon Press, Oxford, 1979, 426 pp. | MR | Zbl

[6] Shramm W., “The Fourier transform of functions of the greatest common divisor”, INTEGERS: Electron. J. Comb. Number Theory, 8 (2008), A50, 7 pp. | MR

[7] Coleman R., Some remarks on Euler's totient function, Cornell Univ., Ithaca, NY, 2012, arXiv: 1207.4446

[8] V. K. Leontiev, Combinatorics and Information, v. 1, Combinatorial Analysis, Mosk. Fiz. Tekh. Inst., M., 2015 (Russian)

[9] H. Bateman, A. Erdélyi, Higher Transcendental Functions, v. 3, McGraw-Hill Book Co., New York, 1953

[10] A. G. Kurosh, A Course in Higher Algebra, Nauka, M., 1968 (Russian) | MR