Cubes in elliptic divisibility sequences

Abstract

Elliptic divisibility sequences 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 and also sequences of Pell numbers are squares or cubes [7, 8]. In [6], we determine in which cases a term of an elliptic divisibility sequence can be a square if one of the first six terms is zero. We also determine the cube terms of these sequences.