Diophantine equations with products of consecutive terms in Lucas sequences

In this paper, we show that if (u(n))(n) >= 1 is a Lucas sequence, then the Diophantine equation u(n) (.) u(n+1) (.....) u(n+k) = y(m) in integers n >= 1, k >=, 4, m >= 2 and y with vertical bar y vertical bar > 1 has only finitely many solutions. We also determine all such solutions when (u(n))(n >= 1) is the sequence of Fibonacci numbers and when u(n) = (x(n) - 1)/(x - 1) for all n >= 1 with some integer x > 1. (c) 2004 Elsevier Inc. All rights reserved.