{"title":"关于Lucas数列中的某些素数","authors":"Ali S. Athab, Hayder R. Hashim","doi":"10.47974/jim-1616","DOIUrl":null,"url":null,"abstract":"In 1964, Shanks conjectured that there are infinitely many primes of the form 1/2(x2 + 1). Therefore, the aim of this paper is to introduce a technique for studying whether or not there are infinitely many prime numbers of the form 1/2(x2 + 1) derived from some Lucas sequences of the first kind {Un(P, Q)} or the second kind {Vn(P, Q)}, where P ≥ 1 and Q = ±1. In addition, as applications we represent the procedure of this technique in case of x is an either integer or Lucas number of the first or the second kind with x ≥ 1 and 1 ≤ P ≤ 20.","PeriodicalId":46278,"journal":{"name":"JOURNAL OF INTERDISCIPLINARY MATHEMATICS","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On certain prime numbers in Lucas sequences\",\"authors\":\"Ali S. Athab, Hayder R. Hashim\",\"doi\":\"10.47974/jim-1616\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In 1964, Shanks conjectured that there are infinitely many primes of the form 1/2(x2 + 1). Therefore, the aim of this paper is to introduce a technique for studying whether or not there are infinitely many prime numbers of the form 1/2(x2 + 1) derived from some Lucas sequences of the first kind {Un(P, Q)} or the second kind {Vn(P, Q)}, where P ≥ 1 and Q = ±1. In addition, as applications we represent the procedure of this technique in case of x is an either integer or Lucas number of the first or the second kind with x ≥ 1 and 1 ≤ P ≤ 20.\",\"PeriodicalId\":46278,\"journal\":{\"name\":\"JOURNAL OF INTERDISCIPLINARY MATHEMATICS\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"JOURNAL OF INTERDISCIPLINARY MATHEMATICS\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.47974/jim-1616\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"JOURNAL OF INTERDISCIPLINARY MATHEMATICS","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.47974/jim-1616","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
In 1964, Shanks conjectured that there are infinitely many primes of the form 1/2(x2 + 1). Therefore, the aim of this paper is to introduce a technique for studying whether or not there are infinitely many prime numbers of the form 1/2(x2 + 1) derived from some Lucas sequences of the first kind {Un(P, Q)} or the second kind {Vn(P, Q)}, where P ≥ 1 and Q = ±1. In addition, as applications we represent the procedure of this technique in case of x is an either integer or Lucas number of the first or the second kind with x ≥ 1 and 1 ≤ P ≤ 20.
期刊介绍：
The Journal of Interdisciplinary Mathematics (JIM) is a world leading journal publishing high quality, rigorously peer-reviewed original research in mathematical applications to different disciplines, and to the methodological and theoretical role of mathematics in underpinning all scientific disciplines. The scope is intentionally broad, but papers must make a novel contribution to the fields covered in order to be considered for publication. Topics include, but are not limited, to the following: • Interface of Mathematics with other Disciplines • Theoretical Role of Mathematics • Methodological Role of Mathematics • Interface of Statistics with other Disciplines • Cognitive Sciences • Applications of Mathematics • Industrial Mathematics • Dynamical Systems • Mathematical Biology • Fuzzy Mathematics The journal considers original research articles, survey articles, and book reviews for publication. Responses to articles and correspondence will also be considered at the Editor-in-Chief’s discretion. Special issue proposals in cutting-edge and timely areas of research in interdisciplinary mathematical research are encouraged – please contact the Editor-in-Chief in the first instance.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
