Tiling the integers with translates of one finite set
Abstract
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), 107111]. 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 February 1998
 DOI:
 10.48550/arXiv.math/9802122
 arXiv:
 arXiv:math/9802122
 Bibcode:
 1998math......2122C
 Keywords:

 Combinatorics;
 Group Theory;
 05B45 (Primary) 11B75;
 20K01 (Secondary)
 EPrint:
 12 pages