Upper bound on the solution to F(2k)n = +F(2k)m with negative subscripts

In this paper, we provide an explicit upper bound on the absolute value of the solutions n < m < 0 to the Diophantine equation F(k)n = ±F(k)m, assuming k is even. Here {F(k)n}n ∈ Z denotes the k-generalized Fibonacci sequence. The upper bound depends only on k.

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Bibliographic Details
Published in:Revista colombiana de matemáticas 2023-04, Vol.56 (2), p.179-187
Main Authors: Pethö, Attila, Szalay, László
Format: Article
Language:English
Subjects:
Diophantine equation
Fibonacci numbers
Sequences
Upper bounds
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Summary:In this paper, we provide an explicit upper bound on the absolute value of the solutions n < m < 0 to the Diophantine equation F(k)n = ±F(k)m, assuming k is even. Here {F(k)n}n ∈ Z denotes the k-generalized Fibonacci sequence. The upper bound depends only on k.
ISSN:0034-7426
2357-4100
DOI:10.15446/recolma.v56n2.108374