On the number of finite additive 2-bases

2026-05-19

AI Summary

This study investigates the asymptotic growth rate of the number of finite additive 2-bases. Departing from conventional approaches rooted in complex analysis, the authors introduce an elementary proof strategy that leverages tools from probability theory and combinatorics. This novel methodology yields a remarkably concise and direct argument, significantly streamlining the derivation while independently confirming the previously established exponential growth result—originally obtained through complex-analytic techniques. The success of this elementary framework not only reinforces the validity of the known asymptotic behavior but also underscores the substantial potential of probabilistic and combinatorial methods in addressing fundamental problems in additive number theory.

Abstract

The number of finite additive 2-bases is known to grow exponentially. While this fact has been established by Marzuola and Miller (2010) using complex analytic techniques embedded in the study of numerical sets, we provide a direct, short proof using elementary probabilistic arguments.

Problem

• finite additive 2-bases
• exponential growth
• numerical sets

Innovation

• additive 2-bases
• exponential growth
• elementary probabilistic arguments
• finite additive bases
• combinatorial number theory