Some Divisibility Properties Concerning Lucas and Elliptic Divisibility Sequences

Abstract

We consider sequences of integers formed by a quotient of the Lucas sequences or elliptic divisibility sequences. We then investigate some divisibility properties of these quotient sequences. Additionally, we prove that elliptic divisibility sequences possess a divisibility property that is analogous to a generalization of Matijasevich’s lemma involving the Fibonacci numbers, which contributed to the solution to Hilbert’s tenth problem.