Let C and W be two sets of integers. If C+W=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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Chen et al. (2024) studied this question.
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