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arXiv · 2001.09634

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

Matteo Verzobio
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Abstract

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 in the form $B_{mp}$ with $p$ a prime congruent to $1$ modulo $4$.

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Matteo Verzobio. 2020-01-27. Primitive divisors of elliptic divisibility sequences for elliptic curves with j=1728. https://doi.org/10.4064/aa191016-30-7

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