On a divisibility relation for Lucas sequences

JOURNAL OF NUMBER THEORY

卷:163

Article

Bilu, Yuri F.^1,2  Komatsu, Takao³  Luca, Florian⁴  Pizarro-Madariaga, Amalia v⁵  Stanica, Pantelimon^6,7 

[1] Univ Bordeaux 1, IMB, 351 Cours Liberat, F-33405 Talence, France

[2] CNRS, 351 Cours Liberat, F-33405 Talence, France

[3] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China

[4] Univ Witwatersrand, Sch Math, Private Bag X3, ZA-2050 Johannesburg, South Africa

[5] Univ Valparaiso, Inst Matemat, Valparaiso, Chile

[6] Naval Postgrad Sch, Dept Appl Math, Monterey, CA 93943 USA

[7] Romanian Acad, Inst Math Simion Stoilow, Bucharest, Romania

关键词: Lucas sequence;    Roots of unity;   

DOI  :  10.1016/j.jnt.2015.11.011

来源: Elsevier

【 摘 要 】

In this note, we study the divisibility relation U-m vertical bar U-n+k(s) -U-n(s), where U := {U-n}(n >= 0) is the Lucas sequence of characteristic polynomial x(2) - ax +/- 1 and k, m, n, s are positive integers. (c) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free