Finding all S-Diophantine quadruples for a fixed set of primes S

Given a finite set of primes S and an m-tuple [Formula: see text] of positive, distinct integers we call the m-tuple S-Diophantine, if for each [Formula: see text] the quantity [Formula: see text] has prime divisors coming only from the set S. For a given set S we give a practical algorithm to find...

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Detalles Bibliográficos
Autor principal: Ziegler, Volker
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Vienna 2021
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8550673/
https://www.ncbi.nlm.nih.gov/pubmed/34776539
http://dx.doi.org/10.1007/s00605-021-01605-w
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author Ziegler, Volker
author_facet Ziegler, Volker
author_sort Ziegler, Volker
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description Given a finite set of primes S and an m-tuple [Formula: see text] of positive, distinct integers we call the m-tuple S-Diophantine, if for each [Formula: see text] the quantity [Formula: see text] has prime divisors coming only from the set S. For a given set S we give a practical algorithm to find all S-Diophantine quadruples, provided that [Formula: see text] .
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spelling pubmed-85506732021-11-10 Finding all S-Diophantine quadruples for a fixed set of primes S Ziegler, Volker Mon Hefte Math Article Given a finite set of primes S and an m-tuple [Formula: see text] of positive, distinct integers we call the m-tuple S-Diophantine, if for each [Formula: see text] the quantity [Formula: see text] has prime divisors coming only from the set S. For a given set S we give a practical algorithm to find all S-Diophantine quadruples, provided that [Formula: see text] . Springer Vienna 2021-07-19 2021 /pmc/articles/PMC8550673/ /pubmed/34776539 http://dx.doi.org/10.1007/s00605-021-01605-w 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
Ziegler, Volker
Finding all S-Diophantine quadruples for a fixed set of primes S
title Finding all S-Diophantine quadruples for a fixed set of primes S
title_full Finding all S-Diophantine quadruples for a fixed set of primes S
title_fullStr Finding all S-Diophantine quadruples for a fixed set of primes S
title_full_unstemmed Finding all S-Diophantine quadruples for a fixed set of primes S
title_short Finding all S-Diophantine quadruples for a fixed set of primes S
title_sort finding all s-diophantine quadruples for a fixed set of primes s
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8550673/
https://www.ncbi.nlm.nih.gov/pubmed/34776539
http://dx.doi.org/10.1007/s00605-021-01605-w
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