Elliptic divisibility sequences over finite fields

Abstract

In this work, we study elliptic divisibility sequences over finite fields. Morgan Ward in [14], [15] gave arithmetic theory of elliptic divisibility sequences and formulas for elliptic divisibility sequences with rank two over finite field F p. We study elliptic divisibility sequences with rank three, four and five over a finite field F p, where p > 3 is a prime and give general terms of these sequences and then we determine elliptic and singular curves associated with these sequences.