Further results on complete permutation monomials over finite fields

TL;DR

This paper constructs new classes of complete permutation monomials over finite fields using the AGW criterion, proving recent conjectures and extending results to more general cases.

Contribution

It introduces new classes of permutation monomials with specific exponents, confirming conjectures and broadening the scope of previous findings.

Findings

Proved two recent conjectures on permutation monomials.

Constructed new classes of permutation monomials using AGW criterion.

Extended results to more general values of n.

Abstract

In this paper, we construct some new classes of complete permutation monomials with exponent $d=\frac{q^n-1}{q-1}$ using AGW criterion (a special case). This proves two recent conjectures in [Wuetal2] and extends some of these recent results to more general $n$'s.