On Finitely Stable Additive Bases

TL;DR

This paper discusses finitely stable additive bases, providing a counterexample to a previous theorem, which may aid in constructing additive bases of specific orders in number theory.

Contribution

It introduces a counterexample to a known theorem on finitely stable additive bases, challenging existing assumptions and aiding future basis construction.

Findings

Counterexample to Theorem 2.2 in previous literature

Insights into the structure of finitely stable additive bases

Potential methods for constructing specific 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.