Explicit solution of a class of quartic Thue equations

1. Introduction. In this paper we deal with the efficient solution of a certain interesting class of quartic Thue equations. In recent years general powerful methods have been developed for the explicit solution of Thue equations; see e.g. [TW], [PS] and the references given there. As these methods depend on rather heavy numerical computations, we think that methods for the solution of special classes of Thue equations which, on the one hand, depend as little as possible on such heavy computations and, on the other hand, are as elementary as possible, have always a theoretical as well as a practical interest. The Thue equations with which we deal in this paper are those equations