Abstract
Let C,W⊆Z. If C+W=Z, then the set C is called an additive complement to W in Z. If no proper subset of C is an additive complement to W, then C is called a minimal additive complement. Let X⊆N. If there exists a positive integer T such that x+T∈X for all sufficiently large integers x∈X, then we call X eventually periodic. In this paper, we study the existence of a minimal complement to W when W is eventually periodic or not. This partially answers a problem of Nathanson.
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