Matsuda monoids and Artin’s primitive root conjecture

Let [Formula: see text] be the additive submonoid generated by 2 and 3. In a recent work, Christensen, Gipson and Kulosman proved that M is not a Matsuda monoid of type 2 and type 3 and they have raised the question of whether M is a Matsuda monoid of type [Formula: see text] for any prime [Formula: see text]. Assuming the generalized Riemann hypothesis, Daileda showed using its’ connection with Artin’s primitive root conjecture that M is not a Matsuda monoid of type [Formula: see text] for any prime [Formula: see text]. In this paper, we will establish this result unconditionally and this resolves the question of Christensen, Gipson and Kulosman.