Cyclotomy, cyclotomic cosets and arithmetic properties of some families in 𝔽l[x] 〈xptq−1〉

Abstract

Arithmetic properties of some families in [Formula: see text] and hence in [Formula: see text] are obtained by using the cyclotomic classes of order 2 with respect to [Formula: see text], where [Formula: see text] is primitive root modulo [Formula: see text], [Formula: see text] and [Formula: see text]. The form of these cyclotomic classes enables us to generalize the results obtained in [S. Jain and S. Batra, Cyclotomy and arithmetic properties of some families in [Formula: see text], Asian-Eur. J. Math. 13(4) (2020) 2050077].