%0 Journal Article
%T Tiling the integers with translates of one finite set
%A Ethan M. Coven
%A Aaron D. Meyerowitz
%J Mathematics
%D 1998
%I arXiv
%X A set is said to tile the integers if and only if the integers can be written as a disjoint union of translates of that set. We consider the problem of finding necessary and sufficient conditions for a finite set to tile the integers. For sets of prime power size, it was solved by D. Newman [J. Number Theory 9 (1977), 107--111]. We solve it for sets of size having at most two prime factors. The conditions are always sufficient, but it is unknown whether they are necessary for all finite sets.
%U http://arxiv.org/abs/math/9802122v1