An Equation Related to k-Generalized Fibonacci Numbers

Result code in IS VaVaI

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Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

An Equation Related to k-Generalized Fibonacci Numbers

Original language description

For k<3, the k-generalized Fibonacci sequence (F_n^{(k)}){n} is defined by the initial values 0,0,ldots,0,1 (k terms) and such that each term afterwards is the sum of the k preceding terms. In this paper, we shall prove that the only solutions of the Diophantine equation F_n^{(k)}=k2^m+1 in positive integers m, n and k<3, are (n,k,m)=(5,2,1), (5,3,1) and (6,3,2). For that, we shall use lower bounds for linear forms in logarithms together with a computational approach using Mathematica software.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

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Continuities

S - Specificky vyzkum na vysokych skolach

Publication year

2016

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Utilitas Mathematica

ISSN

0315-3681

e-ISSN

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Volume of the periodical

101

Issue of the periodical within the volume

November

Country of publishing house

CA - CANADA

Number of pages

11

Pages from-to

79-89

UT code for WoS article

000387834100007

EID of the result in the Scopus database

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