Abstract
For an integer k ≥ 2, let {Fn(k)} n≥2-k be the k-generalized Fibonacci sequence which starts with 0,..., 0, 1 (a total of k terms) and for which each term afterwards is the sum of the k preceding terms. In this paper, we find all integers c with at least two representations as a difference between a k-generalized Fibonacci number and a power of 3. This paper continues the previous work of the first author for the Fibonacci numbers, and for the Tribonacci numbers.
Original language | English |
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Pages (from-to) | 1643-1666 |
Number of pages | 24 |
Journal | International Journal of Number Theory |
Volume | 16 |
Issue number | 7 |
DOIs | |
Publication status | Published - 1 Aug 2020 |
Keywords
- Baker's method
- generalized Fibonacci numbers
- linear forms in logarithms
- Pillai's problem
ASJC Scopus subject areas
- Algebra and Number Theory
Fields of Expertise
- Information, Communication & Computing