PRIME DIVISORS OF SEQUENCES ASSOCIATED TO ELLIPTIC CURVES
Glasgow mathematical journal, Tome 47 (2005) no. 1, pp. 115-122
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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.
EVEREST, GRAHAM; SHPARLINSKI, IGOR E. PRIME DIVISORS OF SEQUENCES ASSOCIATED TO ELLIPTIC CURVES. Glasgow mathematical journal, Tome 47 (2005) no. 1, pp. 115-122. doi: 10.1017/S0017089504002113
@article{10_1017_S0017089504002113,
author = {EVEREST, GRAHAM and SHPARLINSKI, IGOR E.},
title = {PRIME {DIVISORS} {OF} {SEQUENCES} {ASSOCIATED} {TO} {ELLIPTIC} {CURVES}},
journal = {Glasgow mathematical journal},
pages = {115--122},
year = {2005},
volume = {47},
number = {1},
doi = {10.1017/S0017089504002113},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089504002113/}
}
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