Explicit primality criteria for h . 2(n) +/- 1
文献类型：期刊论文
| 作者 | Deng, Yingpu1 ; Huang, Dandan1,2
|
| 刊名 | JOURNAL DE THEORIE DES NOMBRES DE BORDEAUX
 |
| 出版日期 | 2016 |
| 卷号 | 28期号:1页码:55-74 |
| 关键词 | Primality test Generalized Lucasian sequence Reciprocity Law Computational complexity |
| ISSN号 | 1246-7405 |
| 英文摘要 | Let {(T-k(1), . . .T-k(f))}(k >= 0) be a sequence of f-tuples of rational numbers defined from a seed (T-0(1), . . . ,T-0(f)), which is a given initial value, by f recurrences which are polynomials in f variables from the k-th term to deduce the (k + 1)-th term, k >= 0. We describe an algorithm which needs two such sequences with two suitable seeds to determine the primality of numbers h . 2(n) +/- 1, provided h not equal 0 (mod 17), and it runs in deterministic quasi-quadratic time. In particular, when h = 16(m) - 1, m odd, we have a test with two seeds depending only on h, not on n, while the result of Berrizbeitia and Berry (2004) implied that no finite family of seeds for their Lucasian primality test would suffice to test the primality of h . 2(n) +/- 1 for all n. The techniques which we used are Octic and Bioctic Reciprocity Laws. |
| 资助项目 | NNSF of China[11471314] ; NSFC[11401312] ; NSF of the Jiangsu Higher Education Institutions[14KJB110012] ; National Center for Mathematics and Interdisciplinary Sciences, CAS |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000372940600003 |
| 出版者 | UNIV BORDEAUX, INST MATHEMATIQUES BORDEAUX |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/22404]  |
| 专题 | 系统科学研究所 |
| 通讯作者 | Huang, Dandan |
| 作者单位 | 1.Chinese Acad Sci, Acad Math & Syst Sci, NCMIS, Key Lab Math Mechanizat, Beijing 100190, Peoples R China 2.Jinling Inst Technol, Sch Software Engn, Lab Informat Secur, Nanjing 211169, Jiangsu, Peoples R China |
| 推荐引用方式 GB/T 7714 | Deng, Yingpu,Huang, Dandan. Explicit primality criteria for h . 2(n) +/- 1[J]. JOURNAL DE THEORIE DES NOMBRES DE BORDEAUX,2016,28(1):55-74. |
| APA | Deng, Yingpu,&Huang, Dandan.(2016).Explicit primality criteria for h . 2(n) +/- 1.JOURNAL DE THEORIE DES NOMBRES DE BORDEAUX,28(1),55-74. |
| MLA | Deng, Yingpu,et al."Explicit primality criteria for h . 2(n) +/- 1".JOURNAL DE THEORIE DES NOMBRES DE BORDEAUX 28.1(2016):55-74. |
入库方式： OAI收割
来源：数学与系统科学研究院
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