English
Fibonacci numbers and repdigits
Virtualconference
Auteurs : Luca, Florian (Auteur de la Conférence)
CIRM (Editeur )
11A63 - Radix representation; digital problems
11B39 - Fibonacci and Lucas numbers and polynomials and generalizations
11D61 - Exponential equations
CIRM (Editeur )
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Résumé :
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.
Codes MSC : 11A63 - Radix representation; digital problems
11B39 - Fibonacci and Lucas numbers and polynomials and generalizations
11D61 - Exponential equations
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 01/12/2020 Date de captation : 26/11/2020 Sous collection : Research talks arXiv category : Number Theory Domaine : Number Theory Format : MP4 (.mp4) - HD Durée : 00:53:35 Audience : Researchers Download : https://videos.cirm-math.fr/2020-11-26_Luca.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Jean-Morlet Chair 2020 - Conference: Diophantine Problems, Determinism and Randomness / Chaire Jean-Morlet 2020 - Conférence : Problèmes diophantiens, déterminisme et aléatoireOrganisateurs de la rencontre : Rivat, Joël ; Tichy, Robert Dates : 23/11/2020 - 27/11/2020 Année de la rencontre : 2020 URL Congrès : https://www.chairejeanmorlet.com/2256.html
Données de citation
DOI : 10.24350/CIRM.V.19687803Citer cette vidéo: 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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Bibliographie
- 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. -
