December 2023 Products of three Fibonacci numbers that are repdigits
Murat Alan, Kadriye Simsek Alan
Adv. Studies: Euro-Tbilisi Math. J. 16(4): 57-66 (December 2023). DOI: 10.32513/asetmj/193220082333

Abstract

Let $(F_n)_{n\geq 0}$ be a Fibonacci sequence. A non-negative integer whose digits are all equal is called a repdigit and any non-zero repdigit is of the form $ a \left( \dfrac{10^d-1}{9} \right)$ where $ 1 \leq a \leq 9$ and $ 1 \leq d .$ In this paper, we search all repdigits that can be written as products of three Fibonacci numbers. As a mathematical expression, we find all non-negative integer solutions $(n,m,l,a,d)$ of the Diophantine equation $ F_nF_mF_l =a \left( \dfrac{10^d-1}{9} \right),$ $ 1 \leq l \leq m \leq n$ and $1 \leq a \leq 9$.

Funding Statement

This work has been supported by Yildiz Technical University Scientific Research Projects Coordination Unit under project number 4356.

Citation

Download Citation

Murat Alan. Kadriye Simsek Alan. "Products of three Fibonacci numbers that are repdigits." Adv. Studies: Euro-Tbilisi Math. J. 16 (4) 57 - 66, December 2023. https://doi.org/10.32513/asetmj/193220082333

Information

Received: 23 December 2022; Accepted: 7 June 2023; Published: December 2023
First available in Project Euclid: 3 January 2024

Digital Object Identifier: 10.32513/asetmj/193220082333

Subjects:
Primary: 11B39
Secondary: 11D61 , 11J86

Keywords: Diophantine equations , Fibonacci numbers , linear forms in logarithms , repdigits

Rights: Copyright © 2023 Tbilisi Centre for Mathematical Sciences

Vol.16 • No. 4 • September 2023
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