On index divisors and monogenity of certain septic number fields defined by x 7 + ax 3 + b

Abstract

In this paper, for any septic number field K generated by a root α of a monic irreducible trinomial , we describe all prime power divisors of the index of K answering Problem 22 of Narkiewicz [26]. In particular, if , then K is not mongenic. We illustrate our results by some computational examples.