TY - JOUR

T1 - Prime divisors of sequences associated to elliptic curves

AU - Everest, Graham

AU - Shparlinski, Igor E.

PY - 2005/1

Y1 - 2005/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=13744260286&partnerID=8YFLogxK

U2 - 10.1017/S0017089504002113

DO - 10.1017/S0017089504002113

M3 - Article

AN - SCOPUS:13744260286

VL - 47

SP - 115

EP - 122

JO - Glasgow Mathematical Journal

JF - Glasgow Mathematical Journal

SN - 0017-0895

IS - 1

ER -