"Let θ be an algebraic integer and assume that all conjugates of θ, except θ itself, have an absolute value less than 1. Then –θ also has this property; on the other hand, θ is real. Without loss of generality, we may therefore suppose θ ≥ 0. Since the norm of θ is a rational integer, we have θ ≥ 1, except for the trivial case θ = 0. Recently, R. Salem ... discovered the interesting theorem that the set S of all θ is closed and that θ = 1 is an isolated point of S. Consequently there exists a smallest θ = θ1 > 1. We shall prove that θ1 is the positive zero of x3 – x – 1 and that also θ1 is isolated in S. Moreover we shall prove that the next number of S, namely the smallest θ = θ2 > θ1, is the positive zero of x4 – x3 – 1 and that θ2 is again an isolated point of S. Since θ1 = 1.324..., θ2 = 1.380..., both numbers are less than 2½; therefore our statements are contained in the following: . Let θ be an algebraic integer whose conjugates lie in the interior of the unit circle; if ±θ ≠ 0, 1, θ1, θ2, then θ2 > 2."