English

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 y2=x3+axy^2=x^3+ax in minimal form and consider the sequence BnB_n of the denominators of the abscissas of the iterate of a non-torsion point; we show that B5mB_{5m} has a primitive divisor for every mm. Then, we show how to generalize this method to the terms in the form BmpB_{mp} with pp a prime congruent to 11 modulo 44.

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