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http://dx.doi.org/10.4134/CKMS.c160178

FIBONACCI AND LUCAS NUMBERS ASSOCIATED WITH BROCARD-RAMANUJAN EQUATION  

Pongsriiam, Prapanpong (Department of Mathematics, Faculty of Science Silpakorn University)
Publication Information
Communications of the Korean Mathematical Society / v.32, no.3, 2017 , pp. 511-522 More about this Journal
Abstract
We explicitly solve the diophantine equations of the form $$A_{n_1}A_{n_2}{\cdots}A_{n_k}{\pm}1=B^2_m$$, 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 [9] and L. Szalay [13] concerning a variant of Brocard-Ramanujan equation.
Keywords
Fibonacci number; Lucas number; Brocard-Ramanujan equation; Diophantine equation;
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