Primitive divisors of elliptic divisibility sequences

Elliptic divisibility sequences have been introduced by Ward, in 1948. The terms of an elliptic divisibility sequence represent the denominators of the abscissas of the iterates of a point on an elliptic curve. The aim of this thesis is to understand when a term of an elliptic divisibility sequence has a primitive divisor. In the thesis, we prove some explicit results, some uniform results, and we will focus on some particular examples. Moreover, we will study a class of sequences strictly related to elliptic divisibility sequences.