Panraksa C.Mahidol University2023-06-182023-06-182022-01-01Journal of Integer Sequences Vol.25 No.9 (2022)https://repository.li.mahidol.ac.th/handle/20.500.14594/85119We 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.MathematicsArticleSCOPUS2-s2.0-8514064177615307638