Thue equations associated with Ankeny - Brauer - Chowla number fields

For a wide class of one-parameter families of Thue equations of arbitrary degree n ≥ 3 all solutions are determined if the parameter is sufficiently large. The result is based on the Lang - Waldschmidt conjecture, on the primitivity of the associated number fields and on an index bound, which does not depend on the coefficients. By applying the theory of Hilbertian fields and results on thin sets, primitivity is proved for almost all choices (in the sense of density) of the parameters.