Diophantine quadruples with values in k-generalized Fibonacci numbers

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17310%2F18%3AA1901XZY" target="_blank" >RIV/61988987:17310/18:A1901XZY - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.1515/ms-2017-0156" target="_blank" >http://dx.doi.org/10.1515/ms-2017-0156</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1515/ms-2017-0156" target="_blank" >10.1515/ms-2017-0156</a>

Result language

angličtina

Original language name

Diophantine quadruples with values in k-generalized Fibonacci numbers

Original language description

We consider for integers k >= 2 the k-generalized Fibonacci sequences F-(k) := (F-n((k)))(n >= 2-k), whose first k terms are 0, ..., 0, 1 and each term afterwards is the sum of the preceding k terms. In this paper, we show that there does not exist a quadruple of positive integers a1 &lt; a2 &lt; a3 &lt; a4 such that a(i)a(j) + 1 (i not equal j) are all members of F-(k). (C) 2018 Mathematical Institute Slovak Academy of Sciences

Czech name

—

Czech description

—

Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10101 - Pure mathematics

Project

<a href="/en/project/GA17-02804S" target="_blank" >GA17-02804S: Properties of number sequences and their applications</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2018

Confidentiality

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

Name of the periodical

MATHEMATICA SLOVACA

ISSN

0139-9918

e-ISSN

1337-2211

Volume of the periodical

68

Issue of the periodical within the volume

4

Country of publishing house

DE - GERMANY

Number of pages

11

Pages from-to

939-949

UT code for WoS article

000440929900020

EID of the result in the Scopus database

2-s2.0-85051532714