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

11 28

On S-Diophantine Tuples

By Volker Ziegler

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 $|S| = 3$.

Information about the video

Date of recording 23/11/2020
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.19690303
Cite this video Ziegler, Volker (23/11/2020). On S-Diophantine Tuples. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19690303
URL https://dx.doi.org/10.24350/CIRM.V.19690303

Domain(s)

Number Theory

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

MSC codes

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