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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}.
The hyperbolic conics in the hyperbolic geometry
Osman Avcioglu,Osman Bizim 장전수학회 2008 Advanced Studies in Contemporary Mathematics Vol.16 No.1
In this work we have aimed to specify basic properties of hyper-bolic conics of uper half plane U and examined each conic at two steps: Firstly we have studied the case where center and focus(es) of the conic are on imaginary axis. Secondly we have transfered our findings to any conic by means of Mob(U). Although there are works on hyperbolic circles in sources such as[2], we also examine hyperbolic circles for readines. We have also seen that each conic family is invariant under the action of Mob(U).
Inam, Ilker,Soydan, Gokhan,Demirci, Musa,BiZim, Osman,Cangul, Ismail Naci Korean Mathematical Society 2007 대한수학회논문집 Vol.22 No.2
In this work, authors considered a result concerning elliptic curves $y^2=x^3+cx$ over $\mathbb{F}_p$ mod 8, given at [1]. They noticed that there should be a slight change at this result. They give counterexamples and the correct version of the result.