On a Diophantine equation involving powers of Fibonacci numbers

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 identit...

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Bibliographic Details
Main Authors: Gueth Krisztián, Florian Luca (Author), Szalay László (Author)
Format: Article
Published: 2020
Series:PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES 96 No. 4
Subjects:
matematika- és számítástudományok
Online Access:http://publicatio.uni-sopron.hu/1946
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024 7 |a 10.3792/pjaa.96.007  |2 doi 
024 7 |a 31293326  |2 mtmt 
040 |a Soproni Egyetem Publicatio Repozitórium  |b hun 
100 1 |a Gueth Krisztián 
245 1 3 |a On a Diophantine equation involving powers of Fibonacci numbers  |h [elektronikus dokumentum] /  |c Krisztián Gueth 
260 |c 2020 
300 |a 33-37 
490 0 |a PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES  |v 96 No. 4 
520 3 |a 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. 
650 4 |a matematika- és számítástudományok 
700 0 1 |a Florian Luca  |e aut 
700 0 1 |a Szalay László  |e aut 
856 4 0 |u http://publicatio.uni-sopron.hu/1946/1/euclid.pja.1585728123.pdf  |z Dokumentum-elérés  

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