Primitive divisors of sequences associated to elliptic curves

Abstract

Let $\{nP+Q{\}}_{n\ge 0}$ be a sequence of points on an elliptic curve defined over a number field $K$. In this paper, we study the denominators of the $x$-coordinates of this sequence. We prove that, if $Q$ is a torsion point of prime order, then for $n$ large enough there always exists a primitive divisor. Later on, we show the link between the study of the primitive divisors and the Lang-Trotter conjecture.

Cited by in corpus (1)

• Primitive divisors of sequences associated to elliptic curves with complex multiplication