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Fibonacci numbers and repdigits
Virtualconference
Authors : Luca, Florian (Author of the conference)
CIRM (Publisher )
11A63 - Radix representation; digital problems
11B39 - Fibonacci and Lucas numbers and polynomials and generalizations
11D61 - Exponential equations
CIRM (Publisher )
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Abstract :
In the first part of the talk we will survey known results concerning Fibonacci numbers whose digital representations in base 10 display some interesting patterns. In the second part of the talk we will give the main steps of the proof of a recent result which states that $b = 4$ is the only integer ≥ 2 such that there are two Fibonacci numbers larger than 1 which are repunits in base b. In this case, $F_{5}=(4^{2}-1)/(4-1)$ and $F_{8}=(4^{3}-1)/(4-1)$. This is joint work with C. A. Gomez and J. C. Gomez from Cali, Colombia.
MSC Codes : 11A63 - Radix representation; digital problems
11B39 - Fibonacci and Lucas numbers and polynomials and generalizations
11D61 - Exponential equations
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 01/12/2020 Conference Date : 26/11/2020 Subseries : Research talks arXiv category : Number Theory Mathematical Area(s) : Number Theory Format : MP4 (.mp4) - HD Video Time : 00:53:35 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2020-11-26_Luca.mp4 
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Information on the Event
Event Title : Jean-Morlet Chair 2020 - Conference: Diophantine Problems, Determinism and Randomness / Chaire Jean-Morlet 2020 - Conférence : Problèmes diophantiens, déterminisme et aléatoireEvent Organizers : Rivat, Joël ; Tichy, Robert Dates : 23/11/2020 - 27/11/2020 Event Year : 2020 Event URL : https://www.chairejeanmorlet.com/2256.html
Citation Data
DOI : 10.24350/CIRM.V.19687803Cite this video as: Luca, Florian (2020). Fibonacci numbers and repdigits. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19687803 URI : http://dx.doi.org/10.24350/CIRM.V.19687803 |
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Bibliography
- Luca, F. Fibonacci and Lucas numbers with only one distinct digit. Portugal. Math. 57 (2000), no. 2, 243-254. - https://www.emis.de/journals/PM/57f2/pm57f209.pdf
- Bravo, Jhon J.; Luca, Florian On a conjecture about repdigits in k-generalized Fibonacci sequences. Publ. Math. Debrecen 82 (2013), no. 3-4, 623-639. -
