ON m-COVERS AND m-SYSTEMS
ZhiโWei Sun ยท Bulletin of the Australian Mathematical Society ยท 2009
Abstract Let ๐={as(mod ns)}ks=0 be a system of residue classes. With the help of cyclotomic fields we obtain a theorem which unifies several previously known results related to the covering multiplicity of ๐. In particular, we show that if every integer lies in more than m0=โโ ks=11/nsโ members of ๐, then for any a=0,1,2,โฆ there are at least ${m_0\choose \lfloor a/n_0\rfloor }$ subsets I of {1,โฆ,k} with โ sโI1/ns=a/n0. We also characterize when any integer lies in at most m members of ๐, where m is a fixed positive integer.