Abstract Let K = Q (θ) K=Q () be a number field corresponding to the minimal polynomial f (x) = x n + ax n −1 + bx + c over the field Q Q, where θ is an algebraic integer. In this paper, we provide sufficient conditions for i (K) = 1 and i (K) = 2, which give a partial answer to the Narkiewicz Problem 22 for these number fields, where i (K) is the index of K. Finally, we provide examples of infinite families of number fields for which i (K) = 1 and i (K) = 2.
Chatterjee et al. (Fri,) studied this question.