Narayana numbers that are products of two Fibonacci numbers
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913974955540480 |
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| author | Odjoumani, Japhet |
| author_facet | Odjoumani, Japhet |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_02688 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Narayana numbers that are products of two Fibonacci numbers Odjoumani, Japhet Number Theory 11D61, 11D72, 11B39 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. |
| title | Narayana numbers that are products of two Fibonacci numbers |
| topic | Number Theory 11D61, 11D72, 11B39 |
| url | https://arxiv.org/abs/2508.02688 |