The set of k-units modulo n
Let R be a ring with identity, U(R) the group of units of R and k a positive integer. We say that a ∈ U(R) is k-unit if ak = 1. Particularly, if the ring R is Zn, for a positive integer n, we will say that a is a k-unit modulo n. We denote with Uk(n) the set of k-units modulo n. By duk(n) we represe...
- Autores:
-
Caranguay Mainguez, Jhony Fernando
Castillo Gómez, John Hermes
- Tipo de recurso:
- Article of investigation
- Fecha de publicación:
- 2022
- Institución:
- Universidad de Antioquia
- Repositorio:
- Repositorio UdeA
- Idioma:
- eng
- OAI Identifier:
- oai:bibliotecadigital.udea.edu.co:10495/46174
- Acceso en línea:
- https://hdl.handle.net/10495/46174
- Palabra clave:
- Teoría de los números
Numbers, Theory of
Álgebra
Algebra
Conjunto unitario de un anillo
Conjunto unitario de un anillo
Unidad K
Número de carmichael
Número de Knödel
Diagonal property
K-unit
Carmichael number
Knödel number
Propiedad diagonal
- Rights
- openAccess
- License
- http://creativecommons.org/licenses/by-nc-nd/4.0/
| Summary: | Let R be a ring with identity, U(R) the group of units of R and k a positive integer. We say that a ∈ U(R) is k-unit if ak = 1. Particularly, if the ring R is Zn, for a positive integer n, we will say that a is a k-unit modulo n. We denote with Uk(n) the set of k-units modulo n. By duk(n) we represent the number of k-units modulo n and with rduk(n) = φ(n) duk(n) the ratio of k-units modulo n, where φ is the Euler phi function. Recently, S. K. Chebolu proved that the solutions of the equation rdu2(n) = 1 are the divisors of 24. The main result of this work, is that for a given k, we find the positive integers n such that rduk(n) = 1. Finally, we give some connections of this equation with Carmichael’s numbers and two of its generalizations: Knödel numbers and generalized Carmichael numbers. |
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