On the System of Diophantine Equations x (2) − 6y (2) = −5 and x = az (2) − b

Mignotte and Pethö used the Siegel-Baker method to find all the integral solutions (x, y, z) of the system of Diophantine equations x (2) − 6y (2) = −5 and x = 2z (2) − 1. In this paper, we extend this result and put forward a generalized method which can completely solve the family of systems of Di...

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Detalles Bibliográficos
Autores principales: Zhang, Silan, Chen, Jianhua, Hu, Hao
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2014
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4087266/
https://www.ncbi.nlm.nih.gov/pubmed/25045739
http://dx.doi.org/10.1155/2014/632617
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author Zhang, Silan
Chen, Jianhua
Hu, Hao
author_facet Zhang, Silan
Chen, Jianhua
Hu, Hao
author_sort Zhang, Silan
collection PubMed
description Mignotte and Pethö used the Siegel-Baker method to find all the integral solutions (x, y, z) of the system of Diophantine equations x (2) − 6y (2) = −5 and x = 2z (2) − 1. In this paper, we extend this result and put forward a generalized method which can completely solve the family of systems of Diophantine equations x (2) − 6y (2) = −5 and x = az (2) − b for each pair of integral parameters a, b. The proof utilizes algebraic number theory and p-adic analysis which successfully avoid discussing the class number and factoring the ideals.
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spelling pubmed-40872662014-07-20 On the System of Diophantine Equations x (2) − 6y (2) = −5 and x = az (2) − b Zhang, Silan Chen, Jianhua Hu, Hao ScientificWorldJournal Research Article Mignotte and Pethö used the Siegel-Baker method to find all the integral solutions (x, y, z) of the system of Diophantine equations x (2) − 6y (2) = −5 and x = 2z (2) − 1. In this paper, we extend this result and put forward a generalized method which can completely solve the family of systems of Diophantine equations x (2) − 6y (2) = −5 and x = az (2) − b for each pair of integral parameters a, b. The proof utilizes algebraic number theory and p-adic analysis which successfully avoid discussing the class number and factoring the ideals. Hindawi Publishing Corporation 2014 2014-06-17 /pmc/articles/PMC4087266/ /pubmed/25045739 http://dx.doi.org/10.1155/2014/632617 Text en Copyright © 2014 Silan Zhang et al. https://creativecommons.org/licenses/by/3.0/ This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research Article
Zhang, Silan
Chen, Jianhua
Hu, Hao
On the System of Diophantine Equations x (2) − 6y (2) = −5 and x = az (2) − b
title On the System of Diophantine Equations x (2) − 6y (2) = −5 and x = az (2) − b
title_full On the System of Diophantine Equations x (2) − 6y (2) = −5 and x = az (2) − b
title_fullStr On the System of Diophantine Equations x (2) − 6y (2) = −5 and x = az (2) − b
title_full_unstemmed On the System of Diophantine Equations x (2) − 6y (2) = −5 and x = az (2) − b
title_short On the System of Diophantine Equations x (2) − 6y (2) = −5 and x = az (2) − b
title_sort on the system of diophantine equations x (2) − 6y (2) = −5 and x = az (2) − b
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4087266/
https://www.ncbi.nlm.nih.gov/pubmed/25045739
http://dx.doi.org/10.1155/2014/632617
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