  Motzkin posed the problem of finding the maximal density $\mu(M)$ of sets of
integers in which the differences given by a set $M$ do not occur. The problem
is already settled when $|M|\leq 2$ and $M$ is a finite arithmetic progression.
In this paper, we determine $\mu(M)$ when $M$ has some other structure. For
example, we determine $\mu(M)$ when $M$ is a finite geometric progression.
