Integral points on elliptic curves over number fields

Abstract

In recent years there has been an interest in using elliptic logarithms to find integral points on elliptic curves defined over the rationals, see [23], [17], [6] and [12]. This has been partly due to work of David [5], who gave an explicit lower bound for linear forms in elliptic logarithms. Previously, integral points on elliptic curves had been found by Siegel's method; that is, a reduction to a set of Thue equations which could be solved, in principle, by the methods in [19]. For examples of this method see [3], [7], [16], [18], [21], [22] and [8]. Other techniques can be used to find all integral points in some special cases, see, for instance, [14].