The p -adic generalization of the Thue-Siegel-Roth theorem

It was proved recently by Roth that if α is any real algebraic number, and κ > 2, then the inequality has only a finite number of solutions in integers h and q , where q > 0 and ( h , q ) = 1. This remarkable result answered finally a question which had been only partially answered by the work of Thue and Siegel.