Prime divisors of sequences associated to elliptic curves
Number Theory
2007-05-23 v1
Abstract
We consider the primes which divide the denominator of the x-coordinate of a sequence of rational points on an elliptic curve. It is expected that for every sufficiently large value of the index, each term should be divisible by a primitive prime divisor, one that has not appeared in any earlier term. Proofs of this are known in only a few cases. Weaker results in the general direction are given, using a strong form of Siegel's Theorem and some congruence arguments. Our main result is applied to the study of prime divisors of Somos sequences.
Cite
@article{arxiv.math/0404129,
title = {Prime divisors of sequences associated to elliptic curves},
author = {Graham Everest and Igor E Shparlinski},
journal= {arXiv preprint arXiv:math/0404129},
year = {2007}
}