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arXiv · 2602.14447

Tribonacci Numbers That Are Products of Two Lucas Numbers

Ama Ahenfoa Quansah
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Abstract

Let $T_{k}$ be the $k^{\textrm{th}}$ Tribonacci number and $L_{n}$ be the $n^{\textrm{th}}$ Lucas number defined by their respective recurrence relation $T_{k}=T_{k-1}+T_{k-2}+T_{k-3}$ and $L_{n}=L_{n-1}+L_{n-2}$. In this study, we solve the Diophantine equation $T_{k} = L_{m}L_{n}$ for positive integer unknowns $m$, $n$, and $k$ and prove our results.

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Ama Ahenfoa Quansah. 2026-02-16. Tribonacci Numbers That Are Products of Two Lucas Numbers. https://arxiv.org/abs/2602.14447

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