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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}.
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참고문헌 (15)
참고문헌 신청
M. Ayad / 1993 / Periodicite (mod q) des suites elliptiques et points S-entiers sur les courbes elliptiques / Ann. Inst. Fourier (Grenoble) 43(3):585~618
U. Cerruti / 1995 / R-algebras of linear recurrent sequences / J. Algebra 175(1):332~338
D. V. Chudnovsky / 1986 / Sequences of numbers generated by addition in formal groups and new primality and factorization tests / Adv. in Appl. Math. 7(4):385~434
G. Everest / 2003 / Recurrence Sequences, Mathematical Surveys and Monographs, 104
R. Gottfert / 1995 / On the minimal polynomial of the product of linear recurring sequences / Finite Fields Appl. 1(2):204~218
U. Cerruti / 1995 / R-algebras of linear recurrent sequences / J. Algebra 175(1):332~338
D. V. Chudnovsky / 1986 / Sequences of numbers generated by addition in formal groups and new primality and factorization tests / Adv. in Appl. Math. 7(4):385~434
G. Everest / 2003 / Recurrence Sequences, Mathematical Surveys and Monographs, 104
R. Gottfert / 1995 / On the minimal polynomial of the product of linear recurring sequences / Finite Fields Appl. 1(2):204~218
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