P. Das

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math.NT2026

Repdigits as Product of Consecutive Shifted Tribonacci Numbers

Pranabesh Das, Salah Eddine Rihane, Alain TogbÃ©

A repdigit is a positive integer that has only one distinct digit in its decimal expansion, i.e., a number has the form $d (1 0^{m} - 1) /9$ for some $m \geq 1$ and $1 \leq d \leq 9$ . Let…

math.NT2025

Products of Tribonacci Numbers that are the Products of Factorials

Pranabesh Das, J. C. Saunders

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 Alahmad…

math.NT2025

On Pell numbers representable as product of two generalized Fibonacci numbers

Jhon J. Bravo, Pranabesh Das, Jose L. Herrera +1

A generalization of the well-known Fibonacci sequence is the $k$ -Fibonacci sequence with some fixed integer $k \geq 2$ . The first $k$ terms of this sequence are $0, 0, \dots, 1$ , and…