Let C be an irreducible algebraic curve defined over a number field and
inside an algebraic torus of dimension at least 3. We partially answer a
question posed by Levin on points on C for which a non-trivial power lies
again on C. Our results have connections to Zilber's Conjecture on
Intersections with Tori and yield to methods arising in transcendence theory
and the theory of o-minimal structures.Comment: Published version, but with an error fixed in the formula for the
function on page
