Izvorni znanstveni članak

https://doi.org/10.3336/gm.56.1.02

Some arithmetic functions of factorials in Lucas sequences

Eric F. Bravo orcid.org/0000-0003-2191-3776 ; Departamento de Matemáticas, Universidad del Cauca, Calle 5 No. 4-70 Popayán, Colombia
Jhon J. Bravo orcid.org/0000-0001-7772-9260 ; Departamento de Matemáticas, Universidad del Cauca, Calle 5 No. 4-70 Popayán, Colombia

Sažetak

We prove that if {un}n≥ 0 is a nondegenerate Lucas sequence, then there are only finitely many effectively computable positive integers n such that |un|=f(m!), where f is either the sum-of-divisors function, or the sum-of-proper-divisors function, or the Euler phi function. We also give a theorem that holds for a more general class of integer sequences and illustrate our results through a few specific examples. This paper is motivated by a previous work of Iannucci and Luca who addressed the above problem with Catalan numbers and the sum-of-proper-divisors function.

Ključne riječi

Lucas sequence, arithmetic function, Diophantine equation

Hrčak ID:

259298

URI

https://hrcak.srce.hr/259298

Datum izdavanja:

24.6.2021.

Posjeta: 1.027 *