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Prime divisors of sequences associated to elliptic curves

Graham Everest·Igor E Shparlinski
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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.

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Graham Everest, Igor E Shparlinski. 2004-04-06. Prime divisors of sequences associated to elliptic curves. https://arxiv.org/abs/math/0404129

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