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References [1] Elliott , P. D. T. A . Probabilistic Number Theory I .. Grund. der Math. Wiss ., 239 , Springer-Verlag , New York, Berlin , 1979 . [2] Grosswald , E . Representations of Integers as Sums of Squares . Springer , 2011 . [3

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] G aal , I. and R emete , L. , Integral bases and monogenity of pure fields , Journal of Number Theory , 173 ( 2017 ), 129 – 146 . [6] G aál , I. and R emete

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. Multiplicative number theory, Lectures in advanced mathematics , 1 , Markham Pubishing C ., Chicago , 1967 . [5] Debruyne G ., and Vindas , J . On PNT equivalences for Beurling numbers . Monatsh. Math . 184 , 3 ( 2017 ), 401 – 424 . [6] Debruyne

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Decker, W., Greuel, G.-M. and Pfister, G. , Primary Decomposition: Algorithms and Comparisons, in: Algorithmic Algebra and Number Theory , Springer, 187–220 (1998). Pfister G

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