A Diophantine Equation With Powers of Three Consecutive k-Fibonacci Numbers
| dc.contributor.author | Gómez, Carlos A. | |
| dc.contributor.author | Gómez, Jhonny C. | |
| dc.contributor.author | Luca, Florian | |
| dc.date.accessioned | 2025-07-08T21:47:31Z | |
| dc.date.available | 2025-07-08T21:47:31Z | |
| dc.date.issued | 2024 | |
| dc.description.abstract | The k–generalized Fibonacci sequence {Fn(k)}n≥2-k is the linear recurrent sequence of order k whose first k terms are 0,…,0,1 and each term afterwards is the sum of the preceding k terms. The case k=2 corresponds to the well known Fibonacci sequence {Fn}n≥0. In this paper we extend the study of the exponential Diophantine equation Fn+1x+Fnx-Fn-1x=Fm with terms Fr(k) instead of Fr, where r∈{n+1,n,n-1,m}. | |
| dc.identifier.citation | Gómez, C.A., Gómez, J.C. & Luca, F. A Diophantine Equation With Powers of Three Consecutive Fibonacci Numbers. Results Math 79, 136 (2024). https://doi.org/10.1007/s00025-024-02156-w | |
| dc.identifier.issn | 14226383 | |
| dc.identifier.uri | https://repositorio.usc.edu.co/handle/20.500.12421/7290 | |
| dc.language.iso | en | |
| dc.publisher | Birkhauser | |
| dc.subject | 11B39 | |
| dc.subject | 11D61 11J86 | |
| dc.subject | exponential Diophantine equation | |
| dc.subject | Fibonacci numbers | |
| dc.subject | lower bounds for nonzero linear forms in logarithms of algebraic numbers | |
| dc.title | A Diophantine Equation With Powers of Three Consecutive k-Fibonacci Numbers | |
| dc.type | Article |
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