Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024
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Commun. Korean Math. Soc. 2017; 32(3): 511-522

Online first article June 7, 2017      Printed July 31, 2017

https://doi.org/10.4134/CKMS.c160178

Copyright © The Korean Mathematical Society.

Fibonacci and Lucas Numbers Associated with Brocard-Ramanujan Equation

Prapanpong Pongsriiam

Silpakorn University

Abstract

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We explicitly solve the diophantine equations of the form $$ A_{n_1}A_{n_2}\cdots A_{n_k}\pm 1 = B_m^2, $$ where $(A_n)_{n\geq 0}$ and $(B_m)_{m\geq 0}$ are either the Fibonacci sequence or Lucas sequence. This extends the result of D. Marques \cite{Mar} and L. Szalay \cite{Sza} concerning a variant of Brocard-Ramanujan equation.

Keywords: Fibonacci number, Lucas number, Brocard-Ramanujan equation, Diophantine equation

MSC numbers: Primary 11B39; Secondary 11D99

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