On common factors within a series of consecutive terms of an elliptic divisibility sequence

We prove that for any elliptic divisibility sequence and any sufficiently large integer k, one can find k consecutive terms of the sequence such that none of these terms is coprime to all the others. In other words, elliptic divisibility sequences are Pillai sequences, named for a problem posed originally by Pillai for the sequence of integers. In fact we give an upper bound for the smallest value k0 past which this property is valid. We also provide a more general theorem where the coprimality condition is severely relaxed. In case of some particular sequences we give the values of k0, as well.