On a Diophantine equation involving powers of Fibonacci numbers

Gueth Krisztián and Florian Luca and Szalay László (2020) On a Diophantine equation involving powers of Fibonacci numbers. PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 96 (4). pp. 33-37. ISSN 0386-2194

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Official URL: http://doi.org/10.3792/pjaa.96.007

Abstract

This paper deals with the diophantine equation F-1(p) + 2F(2)(p )+ . . . + kF(k)(p) = F-n(q), an equation on the weighted power terms of Fibonacci sequence. For the exponents p, q is an element of {1, 2} the problem has already been solved in ad hoc ways using the properties of the summatory identities appear on the left-hand side of the equation. Here we suggest a uniform treatment for arbitrary positive integers p and q which works, in practice, for small values. We obtained all the solutions for p, q <= 10 by testing the new approach.

Tudományterület / tudományág

natural sciences > mathematics and computer sciences

Faculty

Not relevant

Institution

Soproni Egyetem

Item Type: Article
Additional Information: Funding Agency and Grant Number: Number Theory Focus Area Grant of CoEMaSS at Wits (South Africa); Hungarian National Foundation for Scientific Research GrantOrszagos Tudomanyos Kutatasi Alapprogramok (OTKA) [128088]; Max Planck Institute for Mathematics in Bonn, Germany Funding text: The work on this paper started when the last author visited School of Mathematics of the Wits University. He thanks this Institution for support, and also thanks Kruger Park for excellent working conditions. F. L. was supported in part by the Number Theory Focus Area Grant of CoEMaSS at Wits (South Africa). Part of this work was done when this author visited the Max Planck Institute for Mathematics in Bonn, Germany from September 2019 to February 2020. He thanks this Institution for hospitality and support. For L. Sz. the research was supported by Hungarian National Foundation for Scientific Research Grant No. 128088. This presentation has been made also in the frame of the "EFOP-3.6.1-16-2016-00018 -Improving the role of the research + development + innovation in the higher education through institutional developments assisting intelligent specialization in Sopron and Szombathely''.
SWORD Depositor: Sword Teszt
Depositing User: Horváth Csaba
Identification Number: MTMT:31293326
Date Deposited: 2020. Aug. 13. 10:57
Last Modified: 2020. Aug. 13. 10:57
URI: http://publicatio.uni-sopron.hu/id/eprint/1946

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