Prime divisors of sequences associated to elliptic curves

Graham Everest*, Igor E. Shparlinski

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)
9 Downloads (Pure)

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.

Original languageEnglish
Pages (from-to)115-122
Number of pages8
JournalGlasgow Mathematical Journal
Volume47
Issue number1
DOIs
Publication statusPublished - Jan 2005

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