Fibonacci and Lucas Numbers Associated with Brocard-Ramanujan Equation

Prapanpong Pongsriiam

Published 2015-09-25Version 1

We 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 recent result of Marques (2011) and Szalay (2012) published in Portugaliae Mathematica.