Let $lpha $ be an algebraic number with no nonnegative conjugates over the field of the rationals. Settling a recent conjecture of Kuba, Dubickas proved that the number $lpha$ is a root of a polynomial, say $P$, with positive rational coefficients. We give in this note an upper bound for the degree of $P$ in terms of the discriminant, the degree and the Mahler measure of $lpha$; this answers a question of Dubickas.
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机译：设$ alpha $是在有理数域上没有非负共轭的代数数。杜比卡斯（Dubickas）解决了最近对库巴（Kuba）的猜想，证明了数字 alpha $是多项式的根，例如$ P $，具有正有理系数。我们在本注释中给出了$ P $的度数的上限，以度，度和马勒测度$ alpha $表示;这回答了杜比卡斯的问题。
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