OPERATIONS ON ELLIPTIC DIVISIBILITY SEQUENCES

BİZİM O., GEZER B.

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, vol.55, no.3, pp.763-776, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 55 Issue: 3
  • Publication Date: 2018
  • Doi Number: 10.4134/bkms.b170227
  • Journal Name: BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.763-776
  • Keywords: elliptic divisibility sequences, operations on bilinear sequences, periodicity properties of product sequences, elliptic curves, CURVES
  • Bursa Uludag University Affiliated: Yes

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 [9, Theorem 4].