- Hacettepe Journal of Mathematics and Statistics
- Vol: 38 Issue: 2
- ELLIPTIC DIVISIBILITY SEQUENCES IN CERTAIN RANKS OVER FINITE FIELDS
ELLIPTIC DIVISIBILITY SEQUENCES IN CERTAIN RANKS OVER FINITE FIELDS
Authors : B. Gezer, O. Bizim
Pages : 161-171
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Publication Date : 2009-02-01
Article Type : Research
Abstract :We develop techniques first studied by Morgan Ward to characterize sequences which arise from elliptic curves and which contain a zero term. We first define elliptic divisibility sequences over finite fields by noting that they are not the sequences which arise by reduction from integer sequences. After that, we give general terms of these sequences over the finite fields Fp (p > 3 is a prime) and then we determine elliptic curves and singular curves associated with them.Keywords : Elliptic divisibility sequences, Singular sequences, Elliptic curves, Singular curves, 2000 AMS Classification: 11 B 50