椭圆可整除序列的原始除数的一些有效性结果

Pub Date : 2023-11-03 DOI:10.2140/pjm.2023.325.331
Matteo Verzobio
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Some effectivity results for primitive divisors of elliptic divisibility sequences
Let $P$ be a non-torsion point on an elliptic curve defined over a number field $K$ and consider the sequence $\{B_n\}_{n\in \mathbb{N}}$ of the denominators of $x(nP)$. We prove that every term of the sequence of the $B_n$ has a primitive divisor for $n$ greater than an effectively computable constant that we will explicitly compute. This constant will depend only on the model defining the curve.
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