Primitive divisors of elliptic divisibility sequences for elliptic curves with j=1728

Abstract

Take a rational elliptic curve defined by the equation $y^2=x^3+ax$ in minimal form and consider the sequence $B_n$ of the denominators of the abscissas of the iterate of a non-torsion point; we show that $B_{5m}$ has a primitive divisor for every $m$. Then, we show how to generalize this method to the terms in the form $B_{mp}$ with $p$ a prime congruent to $1$ modulo $4$.

Final version of the paper. Published in Acta Arithmetica

References in corpus (1)

• Primitive divisors of elliptic divisibility sequences

Cited by in corpus (1)

• Some effectivity results for primitive divisors of elliptic divisibility sequences