Elliptic Divisibility Sequences, Squares and Cubes

2011/01/20 by Betül Gezer, Gezer, Betül
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1101.3839

arxiv created 2011/09/23 · arxiv updated 2011/09/26

Abstract

Elliptic divisibility sequences (EDSs) are generalizations of a class of integer divisibility sequences called Lucas sequences. There has been much interest in cases where the terms of Lucas sequences are squares or cubes. In this work, using the Tate normal form having one parameter of elliptic curves with torsion points, the general terms and periods of all elliptic divisibility sequences with a zero term are given in terms of this parameter by means of Mazur's theorem, and it is shown that which term of h_n of an EDS can be a square or a cube by using the general terms of these sequences.

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