Abstract
We consider the sequence of distances to the nearest integer parallel to lambda alpha(n)parallel to, n = 1, 2, 3, ... , where lambda is a real number and a is a Salem number. We prove a characterization of the numbers lambda satisfying the inequality lim sup(n ->infinity) parallel to lambda alpha(n)parallel to < epsilon, where epsilon is an element of ]0, C(alpha)] and C(alpha) is the inverse of the length of the minimal polynomial of alpha. This allows us to extend a related result, on Salem numbers, due to A. H. FAN and J. SCHMELING [5].