Let f(x) = xⁿ-ax^m-b be a monic irreducible polynomial of degree n having integer coefficients. Let K = Q(θ) be an algebraic number field with θ a root of f(x). In this paper, we provide some explicit conditions involving only a, b, m, n for which K is not monogenic. Further, as an application, in a special case, we show that if p is a prime number of the form 32k+1, k ∈ Z and θ is a root of a monic polynomial x³²ⁿ-64ax^m-p with n odd and a divisible by p, then Q(θ) is not monogenic.

The author is supported by the SERB Start-up Research Grant SRG/2021/000393.