Fibonacci factoriangular numbers

被引：7

作者：

Gomez Ruiz, Carlos Alexis ^{[1
]}

Luca, Florian ^{[2
,3
]}

机构：

[1] Univ Valle, Dept Matemat, Calle 13 100-00, Cali 25360, Colombia

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

[3] Univ Ostrava, Dept Math, Fac Sci, 30 Dubna 22, CZ-70103 Ostrava 1, Czech Republic

来源：

INDAGATIONES MATHEMATICAE-NEW SERIES | 2017年 / 28卷 / 04期

关键词：

Fibonacci numbers; Factoriangular numbers; p-adic linear forms in logarithms of algebraic numbers;

D O I：

10.1016/j.indag.2017.05.002

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let (F-m)(m)>= 0 be the Fibonacci sequence given by F-0 = 0, F-1 = 1 and Fm+2 = Fm+1 + Fm, for all m >= 0. In Castillo (2015), it is conjectured that 2, 5 and 34 are the only Fibonacci numbers of the form n! + n (n+1)/2, for some positive integer n. In this paper, we confirm the above conjecture. (C) 2017 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.

引用

页码：796 / 804

页数：9

共 16 条

[1]

[Anonymous], 2015, ASIA PAC J MULTIDISC

[2]

[Anonymous], 1969, FIBONACCI QUART

[3] Effective lower bounds of the p-adic distance between powers of algebraic numbers [J].

Bugeaud, Y ;

Laurent, M .

JOURNAL OF NUMBER THEORY, 1996, 61 (02) :311-342

[4] Classical and modular approaches to exponential Diophantine equations I. Fibonacci and Lucas perfect powers [J].

Bugeaud, Yann ;

Mignotte, Maurice ;

Siksek, Samir .

ANNALS OF MATHEMATICS, 2006, 163 (03) :969-1018

[5]

Cohn J. H., 1964, Proc. Lond. Math. Soc., V39, P537, DOI 10.1112/jlms/s1-39.1.537

[6]

Ljunggren W., 1952, NORSKE VID SELSK FOR, V24, P82

[7] Fibonacci numbers of the form k2+k+2 [J].

Luca, F .

APPLICATIONS OF FIBONACCI NUMBERS, VOL 8, 1999, :241-249

[8]

Luca F., 2000, Portugal. Math, V57, P243

[9]

LUO M, 1989, FIBONACCI QUART, V27, P98

[10]

PETHO A, 1983, PUBL MATH-DEBRECEN, V30, P117

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