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Let K be a number field. In the terminology of Nagell a unit ε of K is called exceptional if 1−ε is also a unit. The existence of such a unit is equivalent to the fact that the unit equation ε1+ε2+ε3=0 is solvable in units ε1,ε2,ε3 of K. Numerous number fields have exceptional units. They have been investigated by many authors, and they have important applications.In this paper we deal with a generalization...