  We show that three problems involving linear difference equations with
rational function coefficients are essentially equivalent. The first problem is
the generalization of the classical Skolem-Mahler-Lech theorem to rational
function coefficients. The second problem is the question whether or not for a
given linear difference equation there exists a Picard-Vessiot extension inside
the ring of sequences. The third problem is a certain special case of the
dynamical Mordell-Lang conjecture. This allows us to deduce solutions to the
first two problems in a particular but fairly general special case.
