On the structure of the sumsets (Q626854)

Let \(k\geq 3\), \(A=\{a_0,a_1,\dots,a_{k-1}\}\) a finite set of integers such that \(0=a_0<a_1<\dots a_{k-1}\) and \((a_0,\dots,a_{k-1})=1.\) The authors prove that there exist integers \(c\) and \(d\) and sets \(C\subseteq [0,c-2]\) and \(D\subseteq [0,d-2]\) such that \[ hA=C\cup [c,ha_{k-1}-d]\cup (ha_{k-1}-D) \] for all \(h\geq \sum_{i=2}^{k-1}a_i-k+1\).