Some Criteria for Class Numbers to Be Non-One
Let d be a positive integer which is not a perfect square and n be any nonzero fixed integer. Then, the equation x2−dy2=n is known as the general Pell equation. In this paper, we give some criteria for class numbers of certain real quadratic fields to be greater than one, depending on the solvabilit...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2020/5672983 |
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| author | Ahmad Issa Hasan Sankari |
| author_facet | Ahmad Issa Hasan Sankari |
| author_sort | Ahmad Issa |
| collection | DOAJ |
| description | Let d be a positive integer which is not a perfect square and n be any nonzero fixed integer. Then, the equation x2−dy2=n is known as the general Pell equation. In this paper, we give some criteria for class numbers of certain real quadratic fields to be greater than one, depending on the solvability of the general Pell equation, ideals in quadratic orders, and the period length of the simple continued fraction expansions of d. |
| format | Article |
| id | doaj-art-31166a55e73a4ed0987f8a74b09f467b |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-31166a55e73a4ed0987f8a74b09f467b2025-02-03T01:20:21ZengWileyJournal of Mathematics2314-46292314-47852020-01-01202010.1155/2020/56729835672983Some Criteria for Class Numbers to Be Non-OneAhmad Issa0Hasan Sankari1Department of Mathematics, Tishreen University, Lattakia, SyriaDepartment of Mathematics, Tishreen University, Lattakia, SyriaLet d be a positive integer which is not a perfect square and n be any nonzero fixed integer. Then, the equation x2−dy2=n is known as the general Pell equation. In this paper, we give some criteria for class numbers of certain real quadratic fields to be greater than one, depending on the solvability of the general Pell equation, ideals in quadratic orders, and the period length of the simple continued fraction expansions of d.http://dx.doi.org/10.1155/2020/5672983 |
| spellingShingle | Ahmad Issa Hasan Sankari Some Criteria for Class Numbers to Be Non-One Journal of Mathematics |
| title | Some Criteria for Class Numbers to Be Non-One |
| title_full | Some Criteria for Class Numbers to Be Non-One |
| title_fullStr | Some Criteria for Class Numbers to Be Non-One |
| title_full_unstemmed | Some Criteria for Class Numbers to Be Non-One |
| title_short | Some Criteria for Class Numbers to Be Non-One |
| title_sort | some criteria for class numbers to be non one |
| url | http://dx.doi.org/10.1155/2020/5672983 |
| work_keys_str_mv | AT ahmadissa somecriteriaforclassnumberstobenonone AT hasansankari somecriteriaforclassnumberstobenonone |