Abstract
Let N be a positive rational integer and let P be the set of powers of a Salem number of degree d. We prove that for any alpha is an element of P the fractional parts of the numbers alpha(n)/n, when n runs through the set of positive rational integers, are dense in the unit interval if and only if N <= 2d - 4. We also show that for any a. P the integer parts of the numbers an are divisible by N for infinitely many n if and only if N <= 2d - 3.