Prime divisors of sequences associated to elliptic curves

Details Prime divisors of sequences associated to elliptic curves Prime divisors of sequences associated to elliptic curves

2004-04-06

arxiv.org/abs/math/0404129v1

Mathematics

Number Theory

Scientific paper

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.

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