Primitive Divisors of Certain Elliptic Divisibility Sequences

Details Primitive Divisors of Certain Elliptic Divisibility Sequences Primitive Divisors of Certain Elliptic Divisibility Sequences

2010-09-04

arxiv.org/abs/1009.0872v3

Acta Arith. 151 (2012), 165-190

Mathematics

Number Theory

version accepted for publication. Difference of heights result moved to http://arxiv.org/abs/1104.4645 and improved. Proof sim

Scientific paper

10.4064/aa151-2-2

Let $P$ be a non-torsion point on the elliptic curve $E_{a}: y^{2}=x^{3}+ax$.
We show that if $a$ is fourth-power-free and either $n>2$ is even or $n>1$ is
odd with $x(P)<0$ or $x(P)$ a perfect square, then the $n$-th element of the
elliptic divisibility sequence generated by $P$ always has a primitive divisor.

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