  Let k be a number field, let E/k be an elliptic curve, and let S be a finite
set of places of k contianing the archimedean places. Let F be an algebraic
closure of k. We prove that if a point P in E(F) is nontorsion, then there are
only finitely many torsion points x in E(F) which are S-integral with respect
to P. We also prove an analogue of this for the multiplicative group, and
formulate conjectural generalizations for abelian varieties and dynamical
systems.
