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arXiv · 2407.04388

On a problem of Nathanson on non-minimal additive complements

Shi--Qiang Chen·Yuchen Ding
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Abstract

Let $C$ and $W$ be two sets of integers. If $C+W=\mathbb{Z}$, then $C$ is called an additive complement to $W$. We further call $C$ a minimal additive complement to $W$ if no proper subset of $C$ is an additive complement to $W$. Answering a problem of Nathanson in part, we give sufficient conditions of $W$ which has no minimal additive complements. Our result also extends the prior result of Chen and Yang.

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Shi--Qiang Chen, Yuchen Ding. 2024-07-05. On a problem of Nathanson on non-minimal additive complements. https://arxiv.org/abs/2407.04388

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