ON FINITELY STABLE ADDITIVE BASES
LUCAS Y. OBATA *
Department of Mathematics and Statistics, State University of Ponta Grossa (UEPG), 84030-900, Ponta Grossa, PR, Brazil.
LUAN A. FERREIRA
Institute of Mathematics and Statistics of University of S~ao Paulo, Rua do Matao, 1010, Cidade Universitaria, S~ao Paulo, SP 05508-090, Brazil.
GIULIANO G. LA GUARDIA *
Department of Mathematics and Statistics, State University of Ponta Grossa (UEPG), 84030-900, Ponta Grossa, PR, Brazil.
*Author to whom correspondence should be addressed.
Abstract
The concept of additive basis has been investigated in the literature for several mathematicians which works with number theory. 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 orders.
Keywords: Additive basis, finitely stable basis, order of a basis, Lagrange Theorem