Even perfect numbers among generalized Fibonacci sequences

被引：2

作者：

Facó V. ^{[1
]}

Marques D. ^{[1
]}

机构：

[1] Departamento de Matemática, Universidade de Brasília, Brasília

来源：

Rendiconti del Circolo Matematico di Palermo (1952 -) | 2014年 / 63卷 / 3期

关键词：

Diophantine equations; Generalized Fibonacci sequences; Linear forms in logarithms; Perfect numbers;

D O I：

10.1007/s12215-014-0165-7

中图分类号：

学科分类号：

摘要：

A positive integer (Formula presented.) is said to be a perfect number, if (Formula presented.), where (Formula presented.) is the sum of all positive divisors of (Formula presented.). Luca (Rend Circ Mat Palermo Ser II 49:313–318, 2000) proved that there is no perfect number in the Fibonacci sequence. For (Formula presented.), the (Formula presented.)-generalized Fibonacci sequence (Formula presented.) is defined by the initial values ((Formula presented.) terms) and such that each term afterwards is the sum of the (Formula presented.) preceding terms. In this paper, we prove, among other things, that there is no even perfect numbers belonging to (Formula presented.)-generalized Fibonacci sequences when (Formula presented.). © 2014, Springer-Verlag Italia.

引用

页码：363 / 370

页数：7

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