On the System of Diophantine Equations x2-6y2=-5 and x=az2-b
Joint Authors
Chen, Jianhua
Zhang, Silan
Hu, Hao
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-4, 4 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-06-17
Country of Publication
Egypt
No. of Pages
4
Main Subjects
Medicine
Information Technology and Computer Science
Abstract EN
Mignotte and Pethö used the Siegel-Baker method to find all the integral solutions (x,y,z) of the system of Diophantine equations x2-6y2=-5 and x=2z2-1.
In this paper, we extend this result and put forward a generalized method which can completely solve the family of systems of Diophantine equations x2-6y2=-5 and x=az2-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.
American Psychological Association (APA)
Zhang, Silan& Chen, Jianhua& Hu, Hao. 2014. On the System of Diophantine Equations x2-6y2=-5 and x=az2-b. The Scientific World Journal،Vol. 2014, no. 2014, pp.1-4.
https://search.emarefa.net/detail/BIM-1050434
Modern Language Association (MLA)
Zhang, Silan…[et al.]. On the System of Diophantine Equations x2-6y2=-5 and x=az2-b. The Scientific World Journal No. 2014 (2014), pp.1-4.
https://search.emarefa.net/detail/BIM-1050434
American Medical Association (AMA)
Zhang, Silan& Chen, Jianhua& Hu, Hao. On the System of Diophantine Equations x2-6y2=-5 and x=az2-b. The Scientific World Journal. 2014. Vol. 2014, no. 2014, pp.1-4.
https://search.emarefa.net/detail/BIM-1050434
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1050434