On Finitely Stable Additive Bases

Abstract

The concept of additive basis has been investigated in the literature for several mathematicians which works with number theorem. Recently, the concept of finitely stable additive basis was introduced. In this note we provide a counterexample of the reciprocal of Theorem 2.2 shown in [Ferreira, L.A.: Finite Stable Additive Basis; Bull. Aust. Math. Soc.]. The idea of the construction of such a counterexample can possibly help the process of finding additive bases of some specific order.