Primitive divisors of elliptic divisibility sequences for elliptic curves with j=1728
Verzobio M. 2021. Primitive divisors of elliptic divisibility sequences for elliptic curves with j=1728. Acta Arithmetica. 198(2), 129–168.
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Abstract
Take a rational elliptic curve defined by the equation y2=x3+ax in minimal form and consider the sequence Bn of the denominators of the abscissas of the iterate of a non-torsion point. We show that B5m has a primitive divisor for every m. Then, we show how to generalize this method to the terms of the form Bmp with p a prime congruent to 1 modulo 4.
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Date Published
2021-01-04
Journal Title
Acta Arithmetica
Publisher
Institute of Mathematics, Polish Academy of Sciences
Volume
198
Issue
2
Page
129-168
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Verzobio M. Primitive divisors of elliptic divisibility sequences for elliptic curves with j=1728. Acta Arithmetica. 2021;198(2):129-168. doi:10.4064/aa191016-30-7
Verzobio, M. (2021). Primitive divisors of elliptic divisibility sequences for elliptic curves with j=1728. Acta Arithmetica. Institute of Mathematics, Polish Academy of Sciences. https://doi.org/10.4064/aa191016-30-7
Verzobio, Matteo. “Primitive Divisors of Elliptic Divisibility Sequences for Elliptic Curves with J=1728.” Acta Arithmetica. Institute of Mathematics, Polish Academy of Sciences, 2021. https://doi.org/10.4064/aa191016-30-7.
M. Verzobio, “Primitive divisors of elliptic divisibility sequences for elliptic curves with j=1728,” Acta Arithmetica, vol. 198, no. 2. Institute of Mathematics, Polish Academy of Sciences, pp. 129–168, 2021.
Verzobio M. 2021. Primitive divisors of elliptic divisibility sequences for elliptic curves with j=1728. Acta Arithmetica. 198(2), 129–168.
Verzobio, Matteo. “Primitive Divisors of Elliptic Divisibility Sequences for Elliptic Curves with J=1728.” Acta Arithmetica, vol. 198, no. 2, Institute of Mathematics, Polish Academy of Sciences, 2021, pp. 129–68, doi:10.4064/aa191016-30-7.
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