On the System of Diophantine Equations x2-6y2=-5 and x=az2-b
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...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/632617 |
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| _version_ | 1832565212373319680 |
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| author | Silan Zhang Jianhua Chen Hao Hu |
| author_facet | Silan Zhang Jianhua Chen Hao Hu |
| author_sort | Silan Zhang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-0afdd8b64df24889a9223b45f9792af6 |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-0afdd8b64df24889a9223b45f9792af62025-02-03T01:08:55ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/632617632617On the System of Diophantine Equations x2-6y2=-5 and x=az2-bSilan Zhang0Jianhua Chen1Hao Hu2School of Mathematics and Statistics, Wuhan University, Hubei 430072, ChinaSchool of Mathematics and Statistics, Wuhan University, Hubei 430072, ChinaSchool of Mathematics and Statistics, Wuhan University, Hubei 430072, ChinaMignotte 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.http://dx.doi.org/10.1155/2014/632617 |
| spellingShingle | Silan Zhang Jianhua Chen Hao Hu On the System of Diophantine Equations x2-6y2=-5 and x=az2-b The Scientific World Journal |
| title | On the System of Diophantine Equations x2-6y2=-5 and x=az2-b |
| title_full | On the System of Diophantine Equations x2-6y2=-5 and x=az2-b |
| title_fullStr | On the System of Diophantine Equations x2-6y2=-5 and x=az2-b |
| title_full_unstemmed | On the System of Diophantine Equations x2-6y2=-5 and x=az2-b |
| title_short | On the System of Diophantine Equations x2-6y2=-5 and x=az2-b |
| title_sort | on the system of diophantine equations x2 6y2 5 and x az2 b |
| url | http://dx.doi.org/10.1155/2014/632617 |
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