Fibonacci numbers at most one away from a product of factorials

Diego Marques
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 18, 2012, Number 3, Pages 13—19
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Authors and affiliations

Diego Marques
Department de Mathemática, Universidade de Brasília
Brasília, DF Brazil

Abstract

Let (Fn)n≥0 be the Fibonacci sequence given by F0 = 0; F1 = 1 and Fn+2 = Fn+1 + Fn, for n ≥ 0. In this note, we find all solutions of the Diophantine equation m1! … mk! ± 1 = Fm, where 2 ≤ m1 ≤ … ≤ mk and m ≥ 3.

Keywords

  • Diophantine equation
  • Factorial
  • Fibonacci
  • Brocard—Ramanujan

AMS Classification

  • Primary: 11Dxx
  • Secondary: 11B39

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Cite this paper

APA

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

Chicago

Marques, 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.

MLA

Marques, 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.

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