Abstract
Let {Fn}n≥0 be the sequence of Fibonacci numbers defined by F= 0 , F1= 1 and Fn+2= Fn+1+ Fn for all n≥ 0. In this paper, for an integer d≥ 2 which is square-free, we show that there is at most one value of the positive integer x participating in the Pell equation x2- dy2= ± 4 which is a sum of two Fibonacci numbers, with a few exceptions that we completely characterize.
Original language | English |
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Article number | 58 |
Number of pages | 21 |
Journal | Proceedings of the Indian Academy of Sciences: Mathematical Sciences |
Volume | 130 |
Issue number | 1 |
Early online date | 23 Sept 2020 |
DOIs | |
Publication status | Published - 1 Dec 2020 |
Keywords
- Fibonacci number
- linear form in logarithm
- Pell equation
- reduction method
ASJC Scopus subject areas
- Mathematics(all)
Fields of Expertise
- Information, Communication & Computing