Resumen de On the set of integral solutions of the Pell equation in number fields

Wolfgang A. Schmid

• We investigate the set of integral solutions, over a given number field, of the equation X2 - dY2= 1, where d denotes some non-zero integer of this field. We define an operation on this set such that it is an abelian group and determine the structure of this abelian group in terms of the number of complex and real embeddings of the number field, and the number of positive embeddings of d.