Products of Tribonacci Numbers that are the Products of Factorials

Pranabesh Das; J. C. Saunders

paper

Products of Tribonacci Numbers that are the Products of Factorials

arXiv:2510.06520

Abstract

In 2014 Marques and Lengyel gave all of the solutions to the equation $T_{n} = m!$ , where $T_{n}$ is the $n$ th term of the Tribonacci sequence $0, 1, 1, 2, 4, 7, 13, 24, \dots$ . In 2023 Alahmadi and Luca generalized their result to the equation $T_{n} = m_{1}! m_{2}! \dots m_{k}!$ for every $k \in N$ , where $m_{1} \leq m_{2} \leq \dots \leq m_{k}$ listing all the solutions to this equation. Here we generalize these results further and give all the solutions to $T_{n} T_{n + 1} T_{n + 2} \dots T_{n + r} = m_{1}! m_{2}! \dots m_{k}!$ and $∣ T_{- n} T_{- n - 1} T_{- n - 2} \dots T_{- n - r} ∣ = m_{1}! m_{2}! \dots m_{k}!$ for every $n, r \in N$ , where $m_{1} \leq m_{2} \leq \dots \leq m_{k}$ .