关于Lucas数列中的某些素数

IF 1.1 Q1 MATHEMATICS

JOURNAL OF INTERDISCIPLINARY MATHEMATICS Pub Date : 2023-01-01 DOI:10.47974/jim-1616

Ali S. Athab, Hayder R. Hashim

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引用次数: 0

摘要

在1964年，Shanks推测存在无穷多个1/2(x2 + 1)形式的素数。因此，本文的目的是介绍一种技术，用于研究在P≥1且Q =±1的情况下，从第一类{Un(P, Q)}或第二类{Vn(P, Q)} Lucas序列中是否存在无穷多个1/2(x2 + 1)形式的素数。此外，作为应用，我们给出了该方法在x为整数或x≥1且1≤P≤20的第一类或第二类卢卡斯数时的过程。

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On certain prime numbers in Lucas sequences

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.

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来源期刊

JOURNAL OF INTERDISCIPLINARY MATHEMATICS MATHEMATICS-

CiteScore

2.70

自引率

23.50%

发文量

141

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.