Pondering the Effectiveness of Thue Theorem in Transcendental Number Theory for Application

摘要

In this paper, we give the original form of Thue Theorem. From the original form, we get to a second and third equivalent forms, and from which we prove that the Thue Theorem is actually not that effective, in the sense that, it does not lead to an immediate solution, unless with extra limit, albeit its indisputable important position in the transcendental number theory. Its potential application is mentioned as well.