Journal of Integer Sequences, Vol. 25 (2022), Article 22.9.2

Some Divisibility Properties Concerning Lucas and Elliptic Divisibility Sequences

Chatchawan Panraksa and Aram Tangboonduangjit
Mahidol University International College
Mahidol University
Salaya, Nakhon Pathom 73170


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.

Full version:  pdf,    dvi,    ps,    latex    

(Concerned with sequences A000045 A000225 A006769 A088545.)

Received May 16 2022; revised versions received July 31 2022; August 7 2022. Published in Journal of Integer Sequences, October 28 2022.

Return to Journal of Integer Sequences home page