Primitive divisors of elliptic divisibility sequences for elliptic curves with j=1728
Number Theory
2023-11-16 v3
Abstract
Take a rational elliptic curve defined by the equation in minimal form and consider the sequence of the denominators of the abscissas of the iterate of a non-torsion point; we show that has a primitive divisor for every . Then, we show how to generalize this method to the terms in the form with a prime congruent to modulo .
Keywords
Cite
@article{arxiv.2001.09634,
title = {Primitive divisors of elliptic divisibility sequences for elliptic curves with j=1728},
author = {Matteo Verzobio},
journal= {arXiv preprint arXiv:2001.09634},
year = {2023}
}
Comments
Final version of the paper. Published in Acta Arithmetica