  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.
