Abstract
Let \(n\) be an integer. A Fermat-Euler dynamical system acts on the set of mod-\(n\) residues coprime to \(n\) by multiplication by a constant (which is also coprime to \(n\)). We study the dependence of the period and the number of orbits of this dynamical system on \(n\). Theorems generalizing Fermat's little theorem, as well as empirical conjectures, are given.
Similar content being viewed by others
References
A. S. Markus and V. I. Matsaev, “On the spectral theory of holomorphic operator functions in a Hilbert space,” Funkts. Anal. Prilozhen., 9, No. 1, 76–77 (1975).
A. S. Markus and V. I. Matsaev, “On the spectral properties of holomorphic operator functions in a Hilbert space,” Mat. Issled., 9, No. 4, 79–90 (1974).
P. Halmos, A Hilbert Space Problem Book, Van Nostrand, Princeton, 1967.
Yu. L. Daletskii and M. G. Krein, Stability of Solutions of Differential Equations in a Banach Space [in Russian], Nauka, M., 1970.
A. M. Gomilko and G. V. Radzievskii, “On numerical ranges of a family of commuting operators,” Mat. Zametki, 62, No. 5, 787–791 (1997).
M. A. Krasnosel'skii, Plane Vector Fields [in Russian], GIFML, M., 1963.
Yu. G. Borisovich, B. D. Gel'man, A. D. Myshkis, and V. V. Obukhovskii, “Topological methods in the theory of fixed points of set-valued mappings,” Usp. Mat. Nauk, 35, No. 1, 59–126 (1980).
I. Gohberg and Yu. Laiterer, “The factorization of operator-functions relative to a contour. II. The canonical factorization of operator-functions that are close to the identity operator,” Math. Nachr., 54, 41–74 (1972).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Gomilko, A.M. Factorization of Operator Functions in a Hilbert Space. Functional Analysis and Its Applications 37, 16–20 (2003). https://doi.org/10.1023/A:1022967809530
Issue Date:
DOI: https://doi.org/10.1023/A:1022967809530