A Salem number 
of degree 6 has a minimal polynomial of the following form:
where a,b and c are integers. The trace of 
is
, where the sum is over the six conjugates
of 
, i.e., the six roots of (2.1). Two of these conjugates are 
and
and the remaining conjugates satisfy 
, so a bound on |a| implies
a bound on 
and hence on |b| and |c|. So, for fixed a, there is a finite
set of 
with 
. Observe that
so 
for all Salem numbers of degree 6. In fact, there are no
such numbers with trace -1, 4 with trace 0, 15 with trace 1, and 39 with
trace 2.
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