arXiv:1905.01015 [math.NT]AbstractReferencesReviewsResources
On the problem of Pillai with $k$--generalized Fibonacci numbers and powers of $3$
Mahadi Ddamulira, Florian Luca
Published 2019-05-02Version 1
For an integer $k\geq 2$, let $\{F^{(k)}_{n}\}_{n\geqslant 2-k}$ be the $ k$--generalized Fibonacci sequence which starts with $0, \ldots, 0,1$ (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.
Comments: 20 pages. arXiv admin note: substantial text overlap with arXiv:1707.07519, arXiv:1803.10434, arXiv:1902.03491
Categories: math.NT
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