Diophantine equations in separated variables and polynomial power sums

We consider Diophantine equations of the shape [Formula: see text] , where the polynomials f and g are elements of power sums. Using a finiteness criterion of Bilu and Tichy, we will prove that under suitable assumptions infinitely many rational solutions (x, y) with a bounded denominator are only p...

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Detalles Bibliográficos
Autores principales: Fuchs, Clemens, Heintze, Sebastian
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Vienna 2021
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8550583/
https://www.ncbi.nlm.nih.gov/pubmed/34776538
http://dx.doi.org/10.1007/s00605-021-01560-6
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author Fuchs, Clemens
Heintze, Sebastian
author_facet Fuchs, Clemens
Heintze, Sebastian
author_sort Fuchs, Clemens
collection PubMed
description We consider Diophantine equations of the shape [Formula: see text] , where the polynomials f and g are elements of power sums. Using a finiteness criterion of Bilu and Tichy, we will prove that under suitable assumptions infinitely many rational solutions (x, y) with a bounded denominator are only possible in trivial cases.
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spelling pubmed-85505832021-11-10 Diophantine equations in separated variables and polynomial power sums Fuchs, Clemens Heintze, Sebastian Mon Hefte Math Article We consider Diophantine equations of the shape [Formula: see text] , where the polynomials f and g are elements of power sums. Using a finiteness criterion of Bilu and Tichy, we will prove that under suitable assumptions infinitely many rational solutions (x, y) with a bounded denominator are only possible in trivial cases. Springer Vienna 2021-04-30 2021 /pmc/articles/PMC8550583/ /pubmed/34776538 http://dx.doi.org/10.1007/s00605-021-01560-6 Text en © The Author(s) 2021 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Fuchs, Clemens
Heintze, Sebastian
Diophantine equations in separated variables and polynomial power sums
title Diophantine equations in separated variables and polynomial power sums
title_full Diophantine equations in separated variables and polynomial power sums
title_fullStr Diophantine equations in separated variables and polynomial power sums
title_full_unstemmed Diophantine equations in separated variables and polynomial power sums
title_short Diophantine equations in separated variables and polynomial power sums
title_sort diophantine equations in separated variables and polynomial power sums
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8550583/
https://www.ncbi.nlm.nih.gov/pubmed/34776538
http://dx.doi.org/10.1007/s00605-021-01560-6
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