Terms of generalized Fibonacci sequences that are powers of their orders

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F16%3A50004687" target="_blank" >RIV/62690094:18470/16:50004687 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.1007/s10986-016-9315-2" target="_blank" >http://dx.doi.org/10.1007/s10986-016-9315-2</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10986-016-9315-2" target="_blank" >10.1007/s10986-016-9315-2</a>

Result language

angličtina

Original language name

Terms of generalized Fibonacci sequences that are powers of their orders

Original language description

Let (Fn)n}=0 be the Fibonacci sequence given by Fn+2 = Fn+1 + Fn, for n}=0, where F0 = 0 and F1 = 1. For k >1, the k-generalized Fibonacci sequence (F(k) n )n is defined by the initial values 0, 0, . . . , 0, 1 (k terms) so that each term afterward is the sum of the k preceding terms. In this paper, we prove that the only solution of the Diophantine equation F(k) m = kt with t > 1 and m > k + 1 }= 4 is F_9^(3) = 3^4.

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

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2016

Confidentiality

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

Name of the periodical

Lithuanian mathematical journal

ISSN

0363-1672

e-ISSN

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Volume of the periodical

56

Issue of the periodical within the volume

2

Country of publishing house

DE - GERMANY

Number of pages

30

Pages from-to

219-228

UT code for WoS article

000376644700005

EID of the result in the Scopus database

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