Portugaliae Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
MATHEMATICA
Vol. 63, No. 3, pp. 251-260 (2006)

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$F_1F_2F_3F_4F_5F_6F_8F_{10}F_{12}=11!$

Florian Luca and Pantelimon Stanica

IMATE, UNAM,
Ap. Postal 61-3 (Xangari), CP. 58089 Morelia, Michoacán -- MEXICO
E-mail: fluca@matmor.unam.mx
Auburn University Montgomery, Department of Mathematics,
Montgomery, AL 36124-4023 -- USA
E-mail: pstanica@mail.aum.edu
Current affiliation:
Naval Postgraduate School, Department of Applied Mathematics,
Monterey, CA 93943 -- USA
E-mail: pstanica@nps.edu

Abstract: In this paper, we show that the equality appearing in the title gives the largest solution of the diophantine equation
$$ F_{n_1}\dots F_{n_k}=m_1!\dots m_t!, $$
where $0<n_1<\dots<n_k$ and $1\le m_1\le m_2\le\dots\le m_t$ are integers.

Keywords: Fibonacci numbers; diophantine equations.

Classification (MSC2000): 11B39.; 11D72.

Full text of the article:

Electronic version published on: 7 Mar 2008.

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