On Terms of Generalized Fibonacci Sequences which are Powers of their Indexes

被引：15

作者：

Trojovsky, Pavel ^{[1
]}

机构：

[1] Univ Hradec Kralove, Fac Sci, Dept Math, Hradec Kralove 50003, Czech Republic

来源：

MATHEMATICS | 2019年 / 7卷 / 08期

关键词：

k-generalized Fibonacci sequence; Diophantine equation; linear form in logarithms; continued fraction; DIOPHANTINE EQUATIONS; SUM; NUMBERS; CONJECTURE; LOGARITHMS; SQUARES; FORM;

D O I：

10.3390/math7080700

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The k-generalized Fibonacci sequence (Fn(k))n (sometimes also called k-bonacci or k-step Fibonacci sequence), with k >= 2, is defined by the values 0,0, horizontal ellipsis ,0,1 of starting k its terms and such way that each term afterwards is the sum of the k preceding terms. This paper is devoted to the proof of the fact that the Diophantine equation Fm(k)=mt, with t>1 and m>k+1, has only solutions F-12((2))=122 and F-9(3)=9(2).

引用

页数：10

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