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OPERATIONS ON ELLIPTIC DIVISIBILITY SEQUENCES
Bizim, Osman,Gezer, Betul Korean Mathematical Society 2018 대한수학회보 Vol.55 No.3
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].
Operations on elliptic divisibility sequences
Osman Bizim,Betul Gezer 대한수학회 2018 대한수학회보 Vol.55 No.3
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}.