Let K = ℚ(α) be a number field generated by a complex root α of a monic irreducible polynomial f(x) = x24 – m, with m ≠ 1 is a square free rational integer. In this paper, we prove that if m ≡ 2 or 3 (mod 4) and m ≢∓1 (mod 9), then the number field K is monogenic. If m ≡ 1 (mod 4) or m ≡ 1 (mod 9), then the number field K is not monogenic.
Ahmad, S., Nakahara, T. and Husnine, S. M., Power integral bases for certain pure sextic fields, Int. J. of Number Theory,8v:10 (2014), 2257- 2265.