# ON FINITELY STABLE ADDITIVE BASES

## Main Article Content

## 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

## Article Details

How to Cite

*Asian Journal of Current Research*,

*6*(4), 1-4. Retrieved from https://ikprress.org/index.php/AJOCR/article/view/7199

Section

Original Research Article

## References

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Nathanson NB. Sums of _nite sets of integers. The American Mathematical Monthly. 1972;79:1010-1012.

Nathanson NB. Minimal bases and maximal nonbases in additive number theory. J. Number Theory. 1974;6:324-333.

Nathanson NB. Additive number Theory - inverse problems and the geometry of sumsets. Graduate Texts in Mathematics 165, Springer-Verlag; 1996.

Nathanson NB. Sums of _nite sets of integers, II. E-print: arXiv:2005.10809v3.

Nathanson NB. Thin bases in additive number theory. Discrete Math. 2012;312:2069-2075.

Nathanson NB. Additive systems and a theorem of de Bruijn. The American Mathematical Monthly. 2014;121:5-17.

Tafula C. An extension of the Erdos-Tetali Theorem. E-print arXiv:1807.10200.

Ferreira LA. Finitely stable additive bases. Bull. Aust. Math. Soc. 2018;97:360-362.

Nathanson NB. Sums of _nite sets of integers. The American Mathematical Monthly. 1972;79:1010-1012.

Nathanson NB. Minimal bases and maximal nonbases in additive number theory. J. Number Theory. 1974;6:324-333.

Nathanson NB. Additive number Theory - inverse problems and the geometry of sumsets. Graduate Texts in Mathematics 165, Springer-Verlag; 1996.

Nathanson NB. Sums of _nite sets of integers, II. E-print: arXiv:2005.10809v3.

Nathanson NB. Thin bases in additive number theory. Discrete Math. 2012;312:2069-2075.

Nathanson NB. Additive systems and a theorem of de Bruijn. The American Mathematical Monthly. 2014;121:5-17.

Tafula C. An extension of the Erdos-Tetali Theorem. E-print arXiv:1807.10200.

Ferreira LA. Finitely stable additive bases. Bull. Aust. Math. Soc. 2018;97:360-362.