Diophantine equations with products of consecutive terms in Lucas sequences Original Research Article

In this paper, we show that if (un)ngreater-or-equal, slanted1 is a Lucas sequence, then the Diophantine equation image in integers ngreater-or-equal, slanted1, kgreater-or-equal, slanted1, mgreater-or-equal, slanted2 and y with y>1 has only finitely many solutions. We also determine all such solutions when (un)ngreater-or-equal, slanted1 is the sequence of Fibonacci numbers and when un=(xn-1)/(x-1) for all ngreater-or-equal, slanted1 with some integer x>1.