We give considerable improvements of the previous bounds on the solutions of decomposable form equations. Further, we generalize and make more efficient our earlier method for solving such equations via unit equations. Some applications are also presented to polynomials and algebraic integers of given discriminant and to power integral bases of number fields.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.