Multiplicative Diophantine equations with factors from different Lucas sequences

Let k≥2k≥2 and {un(1)}n≥0,…,{un(k)}n≥0 be k different nondegenerate binary recurrent sequences of integers. In this paper, we show that under certain conditions, there are only finitely many of k  -tuples of the form (un1(1),…,unk(k)) whose contents are multiplicatively dependent. Furthermore, we determine all such instances when k=3k=3 and the three sequences are the sequence of Fibonacci numbers, Pell numbers, and base 10 repunits, respectively.