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
SN - 0017-0895
VL - 47
SP - 115
EP - 122
JO - Glasgow Mathematical Journal
JF - Glasgow Mathematical Journal
IS - 1
ER -