The Sequences of Fibonacci and Lucas for Real Quadratic Number Fields

被引：0

作者：

Lam-Estrada, Pablo ^{[1
]}

Maldonado-Ramirez, Myriam Rosalia ^{[1
,2
]}

Lopez-Bonilla, Jose Luis ^{[3
]}

Zarate, Fausto Jarquin ^{[3
]}

Rajendra, R. ^{[4
]}

Reddy, P. Siva Kota ^{[5
]}

机构：

[1] Inst Politecn Nacl, Escuela Super Fis & Matemat, Dept Matemat, Unidad Zacatenco, Mexico City, Mexico

[2] Inst Politecn Nacl, Escuela Super Ingn Mecan & Electr, Dept Ingenieria Comunicac & Elect, Unidad Zacatenco, Mexico City, Mexico

[3] Univ Autonoma Ciudad Mexico, Acad Matemat, Mexico City, Mexico

[4] Mangalore Univ, Constituent Coll, Field Marshal KM Cariappa Coll, Dept Math, Madikeri 571201, India

[5] JSS Sci & Technol Univ, Sri Jayachamarajendra Coll Engn, Dept Math, Mysuru 570006, India

来源：

BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA | 2025年 / 43卷

关键词：

Algebraic integers; Fibonacci and Lucas numbers; real quadratic fields;

D O I：

10.5269/bspm.68136

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We construct the sequences of Fibonacci and Lucas in any quadratic field Q(root d) with d > 0 square free, noting that the general properties remain valid as those given by the classical sequences of Fibonacci and Lucas for the case d = 5, under the respective variants. For this construction, we use the fundamental unit of Q(root d) and then we observe the generalizations for any unit of Q(root d). Under certain conditions some of these constructions correspond to k-Fibonacci sequence for some k is an element of N. Further, for both sequences, we obtain the generating function, Golden ratio, Binet's formula and some identities that they keep.

引用

页数：15

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