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arXiv · 2104.04808

Sums of $S$-units in sum of terms of recurrence sequences

P. K. Bhoi·S. S. Rout·G. K. Panda
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Abstract

Let $S := \{p_1,\ldots ,p_{\ell}\}$ be a finite set of primes and denote by $\mathcal{U}_S$ the set of all rational integers whose prime factors are all in $S$. Let $(U_n)_{n\geq 0}$ be a non-degenerate linear recurrence sequence with order at least two. In this paper, we provide a finiteness result for the solutions of the Diophantine equation $aU_n + bU_m = z_1 +\cdots +z_r,$ where $n\geq m$ and $z_1, \ldots, z_r\in \mathcal{U}_S$.

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BibTeXRIS

P. K. Bhoi, S. S. Rout, G. K. Panda. 2021-04-10. Sums of $S$-units in sum of terms of recurrence sequences. https://arxiv.org/abs/2104.04808

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