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On S-Diophantine Tuples
Virtualconference
Authors : Ziegler, Volker (Author of the conference)
CIRM (Publisher )
11A51 - "Factorization; primality"
11D61 - Exponential equations
11Y50 - Computer solution of Diophantine equations
CIRM (Publisher )
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Abstract :
Given a finite set of primes $S$ and a m-tuple $(a_{1},...,a_{m})$ of positive, distinct integers we call the m-tuple $S$-Diophantine, if for each 1 ≤ i < j ≤ m the quantity $a_{i}a_{j}+1$ has prime divisors coming only from the set $S$. In this talk we discuss the existence of m-tuples if the set of primes $S$ is small. We will discuss recent results concerning the case that $|S| = 2$ and $|S| = 3$.
Keywords : Diophantine equations; S-unit equations; S-Diophantine tuples
MSC Codes : Keywords : Diophantine equations; S-unit equations; S-Diophantine tuples
11A51 - "Factorization; primality"
11D61 - Exponential equations
11Y50 - Computer solution of Diophantine equations
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 01/12/2020 Conference Date : 23/11/2020 Subseries : Research talks arXiv category : Number Theory Mathematical Area(s) : Number Theory Format : MP4 (.mp4) - HD Video Time : 00:48:07 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2020-11-23_Ziegler.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.19690303Cite this video as: Ziegler, Volker (2020). On S-Diophantine Tuples. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19690303 URI : http://dx.doi.org/10.24350/CIRM.V.19690303 |
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Bibliography
- ZIEGLER, Volker. Finding all $ S $-Diophantine quadruples for a fixed set of primes $ S$. arXiv preprint arXiv:2010.11670, 2020. - https://arxiv.org/abs/2010.11670
