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AbstractIn this paper, we calculate the index of any septic number field K generated by a root α of a monic irreducible trinomial F(x) = x7 + ax4 + b ∈ ℤx. Our approach is based on Engstrom's results and the factorization of any rational prime in K. In such a way we give a complete answer of Problem 22 of Narkiewicz (28) for this family of number fields. As an application of our results, if i(K) ≠ 1, then K is not monogenic. Also, we give generators of power integral bases in some cases where i(K) = 1. Our results are illustrated by some computational examples.Mathematics Subject Classification (2020): 11R0411Y4011R21Key words: Theorem of Dedekindtheorem of Oreprime ideal factorizationNewton polygonindex of a number fieldpower integral basismonogenic
Omar Kchit (Mon,) studied this question.