Some effectivity results for primitive divisors of elliptic divisibility sequences

Abstract

Let $P$ be a non-torsion point on an elliptic curve defined over a number field $K$ and consider the sequence $\{B_n{\}}_{n\in \mathbb{N}}$ of the denominators of $x(nP)$. We prove that every term of the sequence of the $B_n$ has a primitive divisor for $n$ greater than an effectively computable constant that we will explicitly compute. This constant will depend only on the model defining the curve.

Improved exposition and fixed minor issues. Final version of the paper

References in corpus (2)

• Primitive divisors of sequences associated to elliptic curves with complex multiplication
• Primitive divisors of elliptic divisibility sequences for elliptic curves with j=1728

Cited by in corpus (1)

• Remarks on a theorem of Silverman