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Communications in Algebra

Let K=Q(α) be a number field generated by a complex root α of a monic irreducible trinomial F(x)=x5+ax2+b∈Z[x]. In this paper, for every prime integer p, we give necessary and sufficient conditions on a and b so that p is a common index divisor of K. In particular, if any one of these conditions holds, then K is not monogenic.

On common index divisors and monogenity of certain number fields defined by x5 + ax2 + b