hrcak mascot   Srce   HID

Original scientific paper
https://doi.org/10.3336/gm.51.2.02

Mersenne k-Fibonacci numbers

Jhon J. Bravo   ORCID icon orcid.org/0000-0001-7772-9260 ; Departamento de Matemáticas, Universidad del Cauca, Calle 5 No 4-70, Popayán, Colombia
Carlos A. Gómez   ORCID icon orcid.org/0000-0003-1126-2973 ; Departamento de Matemáticas, Universidad del Valle, Calle 13 No 100-00, Cali, Colombia

Fulltext: english, pdf (150 KB) pages 307-319 downloads: 519* cite
APA 6th Edition
Bravo, J.J. & Gómez, C.A. (2016). Mersenne k-Fibonacci numbers. Glasnik matematički, 51 (2), 307-319. https://doi.org/10.3336/gm.51.2.02
MLA 8th Edition
Bravo, Jhon J. and Carlos A. Gómez. "Mersenne k-Fibonacci numbers." Glasnik matematički, vol. 51, no. 2, 2016, pp. 307-319. https://doi.org/10.3336/gm.51.2.02. Accessed 1 Dec. 2021.
Chicago 17th Edition
Bravo, Jhon J. and Carlos A. Gómez. "Mersenne k-Fibonacci numbers." Glasnik matematički 51, no. 2 (2016): 307-319. https://doi.org/10.3336/gm.51.2.02
Harvard
Bravo, J.J., and Gómez, C.A. (2016). 'Mersenne k-Fibonacci numbers', Glasnik matematički, 51(2), pp. 307-319. https://doi.org/10.3336/gm.51.2.02
Vancouver
Bravo JJ, Gómez CA. Mersenne k-Fibonacci numbers. Glasnik matematički [Internet]. 2016 [cited 2021 December 01];51(2):307-319. https://doi.org/10.3336/gm.51.2.02
IEEE
J.J. Bravo and C.A. Gómez, "Mersenne k-Fibonacci numbers", Glasnik matematički, vol.51, no. 2, pp. 307-319, 2016. [Online]. https://doi.org/10.3336/gm.51.2.02

Abstracts
For an integer k≥ 2, let (Fn(k))n be the k-Fibonacci sequence which starts with 0,...,0,1 (k terms) and each term afterwards is the sum of the k preceding terms. In this paper, we find all k-Fibonacci numbers which are Mersenne numbers, i.e., k-Fibonacci numbers that are equal to 1 less than a power of 2. As a consequence, for each fixed k, we prove that there is at most one Mersenne prime in (Fn(k))n.

Keywords
Generalized Fibonacci numbers; Mersenne numbers; linear forms in logarithms; reduction method

Hrčak ID: 170038

URI
https://hrcak.srce.hr/170038

Visits: 784 *