Diego Marques

Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132

Volume 18, 2012, Number 3, Pages 13—19

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## Details

### Authors and affiliations

Diego Marques

*Department de Mathemática, Universidade de Brasília
Brasília, DF Brazil
*

### Abstract

Let (*F _{n}*)

_{n≥0}be the Fibonacci sequence given by

*F*

_{0}= 0;

*F*

_{1}= 1 and

*F*

_{n+2}=

*F*

_{n+1}+

*F*, for

_{n}*n*≥ 0. In this note, we find all solutions of the Diophantine equation

*m*

_{1}! …

*m*! ± 1 =

_{k}*F*, where 2 ≤

_{m}*m*

_{1}≤ … ≤

*m*and

_{k}*m*≥ 3.

### Keywords

- Diophantine equation
- Factorial
- Fibonacci
- Brocard—Ramanujan

### AMS Classification

- Primary: 11Dxx
- Secondary: 11B39

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## Cite this paper

APAMarques, D. (2012). Fibonacci numbers at most one away from a product of factorials, Notes on Number Theory and Discrete Mathematics, 18(3), 13-19.

ChicagoMarques, Diego. “Fibonacci Numbers At Most One Away from a Product of Factorials.” Notes on Number Theory and Discrete Mathematics 18, no. 3 (2012): 13-19.

MLAMarques, Diego. “Fibonacci Numbers At Most One Away from a Product of Factorials.” Notes on Number Theory and Discrete Mathematics 18.3 (2012): 13-19. Print.