Jean-Morlet Chair 2020 - Conference: Diophantine Problems, Determinism and Randomness / Chaire Jean-Morlet 2020 - Conférence : Problèmes diophantiens, déterminisme et aléatoire

Collection Jean-Morlet Chair 2020 - Conference: Diophantine Problems, Determinism and Randomness / Chaire Jean-Morlet 2020 - Conférence : Problèmes diophantiens, déterminisme et aléatoire

Organizer(s) Rivat, Joël ; Tichy, Robert

Date(s) 23/11/2020 - 27/11/2020

linked URL https://www.chairejeanmorlet.com/2256.html

00:00:00 / 00:00:00

8 28

Fibonacci numbers and repdigits

By Florian Luca

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.

Information about the video

Date of recording 26/11/2020
Date of publication 01/12/2020
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19687803
Cite this video Luca, Florian (26/11/2020). Fibonacci numbers and repdigits. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19687803
URL https://dx.doi.org/10.24350/CIRM.V.19687803

Domain(s)

Number Theory

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. -

MSC codes

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