Numbers expressible as a difference of two Pisot numbers

We characterize algebraic integers which are differences of two Pisot numbers. Each such number α must be real and its conjugates over ℚ must all lie in the union of the disc |z|<2 and the strip |(z)|<1 . In particular, we prove that every real algebraic integer α whose conjugates over ℚ , except possibly for α itself, all lie in the disc |z|<2 can always be written as a difference of two Pisot numbers. We also show that a real quadratic algebraic integer α with conjugate α' over ℚ is always expressible as a difference of two Pisot numbers except for the cases α<α'<-2 or 2<α'<α when α cannot be expressed in that form. A similar complete characterization of all algebraic integers α expressible as a difference of two Pisot numbers in terms of the location of their conjugates is given in the case when the degree d of α is a prime number.