OPERATIONS ON ELLIPTIC DIVISIBILITY SEQUENCES


BİZİM O. , GEZER B.

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

  • Publication Type: Article / Article
  • Volume: 55 Issue: 3
  • Publication Date: 2018
  • Doi Number: 10.4134/bkms.b170227
  • Title of Journal : BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY
  • Page Numbers: pp.763-776

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].