Problems in additive number theory, VII: The structure of additive $h$-bases for $n$

Melvyn B. Nathanson

Problems in additive number theory, VII: The structure of additive $h$-bases for $n$

Number Theory 2026-05-28 v2 Combinatorics

Authors: Melvyn B. Nathanson

Abstract

In additive number theory, a finite set $A$ of integers is an $h$ -basis for $n$ if every integer in $\{0,1,2,\ldots, n\}$ can be represented as the sum of exactly $h$ not necessarily distinct elements of $A$ . This paper introduces a new class of problems for these and related additive bases. The problems are designed, in part, to be susceptible to solution by AI.

Keywords

additive number theory h-basis integer representations AI in mathematics combinatorial number theory

Cite

@article{arxiv.2605.26425,
  title  = {Problems in additive number theory, VII: The structure of additive $h$-bases for $n$},
  author = {Melvyn B. Nathanson},
  journal= {arXiv preprint arXiv:2605.26425},
  year   = {2026}
}

Comments

13 pages, new results and problems added

Problems in additive number theory, VII: The structure of additive $h$-bases for $n$

Abstract

Keywords

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