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

نویسندگان

چکیده

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

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ژورنال

عنوان ژورنال: Acta Arithmetica

سال: 2021

ISSN: ['0065-1036', '1730-6264']

DOI: https://doi.org/10.4064/aa191016-30-7