REPRESENTATION OF UNITY BY BINARY FORMS

摘要

In this paper, it is shown that if 17(x, y) is an irreducible binaryform with integral coefficients and degree n ≥3, then provided that the abso-lute value of the discriminant of F is large enough, the equation F(x, y)has at most — 2 solutions in integers x and y. We will also establish somesharper hounds when more restrictions are assumed. These upper houndsare derived by combining methods from classical analysis and geometry ofnumbers. The theory of linear forms in logarithms plays an essential role instudying the geometry of our Diophantine equations.