Abstract Let f (x) = (x^2+1) ^n - ax^n Zx and assume f (x) is irreducible. Let be a root of f (x), set K= Q () and denote by Z₊ the ring of integers of K. The index of f, denoted ind (f), is the index of Z in Z₊. A polynomial f (x) is said to be monogenic if ind (f) = 1. We compute the discriminant of the polynomial f (x), and then derive necessary and sufficient conditions on the parameters a and n for f (x) to be monogenic. Furthermore, we provide a complete description of the primes that divide ind (f).
BARMAN et al. (2026) studied this question.