Operations on elliptic divisibility sequences
Bull. Korean Math. Soc. 2018 Vol. 55, No. 3, 763-776
https://doi.org/10.4134/BKMS.b170227
Published online May 31, 2018
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
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