Integer solutions to decomposable form inequalities Original Research Article

This paper obtains a result on the finiteness of the number of integer solutions to decomposable form inequalities. Let k be a number field and let F(X1,...,Xm) be a non-degenerate decomposable form with coefficients in k. We prove that, for every finite set of places S of k containing the archimedean places of k, for each real number image and for each constant c>0, the inequalityimagehas only finitely many image-non-proportional solutions.