Primitive divisors of elliptic divisibility sequences for elliptic curves with
Tom 198 / 2021
Acta Arithmetica 198 (2021), 129-168
MSC: Primary 11G05, 11B39; Secondary 11A41, 11D59, 11G07, 11G50.
DOI: 10.4064/aa191016-30-7
Opublikowany online: 4 January 2021
Streszczenie
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 of the form B_{mp} with p a prime congruent to 1 modulo 4.