  Assuming Lang's conjectured lower bound on the heights of non-torsion points
on an elliptic curve, we show that there exists an absolute constant C such
that for any elliptic curve E/Q and non-torsion point P in E(Q), there is at
most one integral multiple [n]P such that n > C. The proof is a modification of
a proof of Ingram giving an unconditional but not uniform bound. The new
ingredient is a collection of explicit formulae for the sequence of valuations
of the division polynomials. For P of non-singular reduction, such sequences
are already well described in most cases, but for P of singular reduction, we
are led to define a new class of sequences called elliptic troublemaker
sequences, which measure the failure of the Neron local height to be quadratic.
As a corollary in the spirit of a conjecture of Lang and Hall, we obtain a
uniform upper bound on h(P)/h(E) for integer points having two large integral
multiples.
