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On some diophantine equations in separated variables
Virtualconference
Authors : Bérczes, Attila (Author of the conference)
CIRM (Publisher )
11C08 - Polynomials, See also {13F20}
11D41 - "Higher degree equations; Fermat's equation"
CIRM (Publisher )
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Abstract :
A Diophantine equation has separated variables if it is of the form $ f(x) = g(y)$ for polynomials $f$, $g$. In a more general sense the degree of $f $ and $g$ may also be a variable.In the present talk various results for special types of the polynomials $f$ and $g$ will be presented. The types of the considered polynomials contain power sums, sums of products of consecutive integers, Komornik polynomials, perfect powers. Results on $F$-Diophantine sets, which are proved using results on Diophantine equations in separated variables will also be considered. The main tool for the proof of the presented general qualitative results is the famous Bilu-Tichy Theorem. Further, effective results (which depend on Baker's method) and results containing the complete solutions to special cases of these equations will also be included.
Keywords : Diophantine equation; separated variable; polynomials
MSC Codes : Keywords : Diophantine equation; separated variable; polynomials
11C08 - Polynomials, See also {13F20}
11D41 - "Higher degree equations; Fermat's equation"
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 01/12/2020 Conference Date : 25/11/2020 Subseries : Research talks arXiv category : Number Theory Mathematical Area(s) : Number Theory Format : MP4 (.mp4) - HD Video Time : 00:46:39 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2020-11-25_Berczes.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.19685903Cite this video as: Bérczes, Attila (2020). On some diophantine equations in separated variables. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19685903 URI : http://dx.doi.org/10.24350/CIRM.V.19685903 |
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