On the Index of the Octic Number Field Defined by x8+ax+b

Abstract Let K be an octic number field generated by a complex root θ of a monic irreducible trinomial F(x) = x8 + ax + b ∈ Z[x], where a and b are two non-zero rational integers. Let i(K) be the index of K. In this paper, we show that i(K) is either 1 or a power of 2. Further, we give necessary and suffcient conditions depending only on a and b so that 2 is a prime common index divisor of K. In particular, we provide suffcient conditions for which K is non-monogenic. In such a way our results extend a result proved in [H. Ben Yakkou, On monogenity of certain number fields defned by trinomial of type x8 + ax + b, Acta Math. Hungar. 166 (2022), 614-623], when some suffcient conditions of the divisibility of i(K) by 2 are provided.