In this paper we give an estimate for the difference between the moduli of two roots of a polynomial with integer coefficients in terms of its degree and Mahler measure. An application of this estimate implies a stronger version of a recent result of Gómez Ruiz and Luca. In passing, we prove an estimate for the distance between two algebraic numbers in terms of their degrees and Mahler measures. For possible applications all our results are given with explicit constants. They are stated without any extra conditions or unnecessary assumptions whenever possible.

中文翻译：

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关于两个代数数之间的距离

在本文中，我们针对具有整数系数的多项式的两个根的模数之间的差，根据其程度和马勒测度给出了一个估计。应用此估计值意味着对GómezRuiz和Luca最近的结果进行了更强的描述。顺便说一句，我们证明了两个代数之间的度数和马勒度量的估计。对于可能的应用，我们所有的结果均带有显式常量。声明它们时没有任何额外条件或不必要的假设。