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arXiv · 2508.02688

Narayana numbers that are products of two Fibonacci numbers

Japhet Odjoumani
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Abstract

Let $\{N_m\}_{m\ge0}$ be the Narayana's cows sequence given by $N_0=0$, $N_1=1=N_2=1$ and \[ N_{m+3}=N_{m+2}+N_m,\quad \text{ for }\; m\geq 0 \] and let $\{F_n\}_{n\ge0}$ be the Fibonacci sequence. In this paper we solve explicitely the Diophantine equation \[ N_m=F_nF_k, \] in positive unknowns $m,\,n$ and $k$. That is, we find the non-zero narayana numbers that are products of two Fibonacci numbers.

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Japhet Odjoumani. 2025-07-23. Narayana numbers that are products of two Fibonacci numbers. https://arxiv.org/abs/2508.02688

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