A sharp result on $m$-covers
A sharp result on $m$-covers
Let $A=\{a_{s}+n_{s}\mathbb Z \}_{s=1}^{k}$ be a finite system of residue classes which forms an $m$-cover of $\mathbb Z$ (i.e., every integer belongs to at least $m$ members of $A$). In this paper we show the following sharp result: For any positive integers $m_{1},\ldots ,m_{k}$ and $\theta \in [0,1)$, if there …