Integral Points for Drinfeld Modules

We prove that in the backward orbit of a nonpreperiodic (nontorsion) point under the action of a Drinfeld module of generic characteristic there exist at most finitely many points S-integral with respect to another nonpreperiodic point. This provides the answer (in positive characteristic) to a question raised by Sookdeo in [26]. We also prove that for each nontorsion point z there exist at most finitely many torsion (preperiodic) points which are S-integral with respect to z. This proves a question raised by Tucker and the author in [13], and it gives the analogue of Ih’s conjecture [3] for Drinfeld modules.