Gueth Krisztián and Florian Luca and Szalay László (2020) On a Diophantine equation involving powers of Fibonacci numbers. PROCEEDINGS OF THE JAPAN ACADEMY SERIES AMATHEMATICAL SCIENCES, 96 (4). pp. 3337. ISSN 03862194

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Abstract
This paper deals with the diophantine equation F1(p) + 2F(2)(p )+ . . . + kF(k)(p) = Fn(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 lefthand 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 "EFOP3.6.116201600018 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.unisopron.hu/id/eprint/1946 
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