2004/04/06 by Graham Everest, Everest, Graham, Igor E Shparlinski +1 · 1 citation
Mathematics · #11G05 #11G41 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11G05 #msc:11G41
paper · pdf · doi:10.48550/arxiv.math/0404129
arxiv created 2004/04/06 · arxiv updated 2009/12/01
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.