Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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OPERATIONS ON ELLIPTIC DIVISIBILITY SEQUENCES

  • Bizim, Osman (Uludag University Faculty of Science Department of Mathematics) ;
  • Gezer, Betul (Uludag University Faculty of Science Department of Mathematics)
  • Received : 2017.03.14
  • Accepted : 2018.03.08
  • Published : 2018.05.31
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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].

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References

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