Sumsets of Pisot and Salem numbers

Let S and T be the sets of Pisot and Salem numbers, respectively. We prove that the set mT∩T is empty for every positive integer m 2, i.e., that no sum of several Salem numbers is a Salem number. We also obtain a result which implies that the sets mT∩S and mS∩T are nonempty for every m 2, i.e., that certain Salem numbers can sum to a Pisot number and that certain Pisot numbers can sum to a Salem number. As an explicit example, the Salem number is expressed by a sum of two Pisot numbers.