Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2018; 55(3): 763-776

Online first article May 2, 2018      Printed May 31, 2018

https://doi.org/10.4134/BKMS.b170227

Copyright © The Korean Mathematical Society.

Operations on elliptic divisibility sequences

Osman Bizim, Betul Gezer

Uludag University, Uludag University

Abstract

In this paper we consider the element-wise (Hadamard) product (or sum) of elliptic divisibility sequences and study the periodic structure of \ these sequences. We obtain that the element-wise product (or sum) of elliptic divisibility sequences are periodic modulo a prime $p$ like linear recurrence sequences. Then we study periodicity properties of product sequences. We generalize our results to the case of modulo $p^{l}$ for some prime $p>3$ and positive integer $l$. Finally we consider the $p$-adic behavior of product sequences and give a generalization of \cite[Theorem 4] {JS1}.

Keywords: elliptic divisibility sequences, operations on bilinear sequences, periodicity properties of product sequences, elliptic curves

MSC numbers: 11B37, 11B83, 11G07