ETD

• Elliptic curves
• Elliptic divisibility sequences
• Primitive divisors
• Recurrence 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.