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arXiv · 2403.17953

Solutions to a Pillai-type equation involving Tribonacci numbers and S-units

Herbert Batte·Florian Luca
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Abstract

Let $ \{T_n\}_{n\geq 0} $ be the sequence of Tribonacci numbers. In this paper, we study the exponential Diophantine equation $T_n-2^x3^y=c$, for $n,x,y\in \mathbb{Z}_{\ge0}$. In particular, we show that there is no integer $c$ with at least six representations of the form $T_n-2^x3^y$.

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Herbert Batte, Florian Luca. 2024-03-10. Solutions to a Pillai-type equation involving Tribonacci numbers and S-units. https://arxiv.org/abs/2403.17953

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