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Ratios of sums of two Fibonacci numbers equal to powers of 2

Jhon J. Bravo   ORCID icon orcid.org/0000-0001-7772-9260 ; Departamento de Matemáticas, Universidad del Cauca, Popayán, Colombia
Maribel Díaz ; Departamento de Matemáticas, Universidad del Cauca, Popayán, Colombia
Florian Luca ; School of Mathematics, University of the Witwatersrand, South Africa

Puni tekst: engleski, pdf (144 KB) str. 185-199 preuzimanja: 63* citiraj
APA 6th Edition
Bravo, J.J., Díaz, M. i Luca, F. (2020). Ratios of sums of two Fibonacci numbers equal to powers of 2. Mathematical Communications, 25 (2), 185-199. Preuzeto s https://hrcak.srce.hr/244257
MLA 8th Edition
Bravo, Jhon J., et al. "Ratios of sums of two Fibonacci numbers equal to powers of 2." Mathematical Communications, vol. 25, br. 2, 2020, str. 185-199. https://hrcak.srce.hr/244257. Citirano 24.06.2021.
Chicago 17th Edition
Bravo, Jhon J., Maribel Díaz i Florian Luca. "Ratios of sums of two Fibonacci numbers equal to powers of 2." Mathematical Communications 25, br. 2 (2020): 185-199. https://hrcak.srce.hr/244257
Harvard
Bravo, J.J., Díaz, M., i Luca, F. (2020). 'Ratios of sums of two Fibonacci numbers equal to powers of 2', Mathematical Communications, 25(2), str. 185-199. Preuzeto s: https://hrcak.srce.hr/244257 (Datum pristupa: 24.06.2021.)
Vancouver
Bravo JJ, Díaz M, Luca F. Ratios of sums of two Fibonacci numbers equal to powers of 2. Mathematical Communications [Internet]. 2020 [pristupljeno 24.06.2021.];25(2):185-199. Dostupno na: https://hrcak.srce.hr/244257
IEEE
J.J. Bravo, M. Díaz i F. Luca, "Ratios of sums of two Fibonacci numbers equal to powers of 2", Mathematical Communications, vol.25, br. 2, str. 185-199, 2020. [Online]. Dostupno na: https://hrcak.srce.hr/244257. [Citirano: 24.06.2021.]

Sažetak
In this paper, we find all solutions to the Diophantine equation $F_n+F_m=2^a(F_r+F_s)$, where $\{F_k\}_{k\ge 0}$ is the Fibonacci sequence. This paper continues and extends a previous work which investigated the powers of 2 which are sums of two Fibonacci numbers.

Ključne riječi
Fibonacci number, Zeckendorf representation, linear form in logarithms, reduction method

Hrčak ID: 244257

URI
https://hrcak.srce.hr/244257

Posjeta: 145 *