  Let A be an abelian variety defined over a number field K and let P and Q be
points in A(K) satisfying the following condition: for all but finitely many
primes p of K, the order of (Q mod p) divides the order of (P mod p). Larsen
proved that there exists a positive integer c such that cQ is in the
End_K(A)-module generated by P. We study the minimal value of c and construct
some refined counterexamples.
