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Explicit solution of a class of quartic Thue equations. (English) Zbl 0774.11014

This paper deals with those quartic Thue equations, whose corresponding quartic number fields are Galois and non-cyclic. It is shown that the solution of such equations is reduced to the solution of a system of two Pellian equations and methods are discussed for solving such a system elementarily. The most promising and general of those methods due to R. G. E. Pinch [Math. Proc. Camb. Philos. Soc. 103, 35-46 (1988; Zbl 0641.10014)], is not in fact elementary in that it is based on the theory of linear forms in logarithms of algebraic numbers, but has the advantage that, unlikely most applications of this theory, it completely avoids high precision computations and the use of “long numbers”. As an application, a number of specific equations belonging to the class under consideration are explicitly solved.

MSC:

11D25 Cubic and quartic Diophantine equations

Citations:

Zbl 0641.10014
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