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Algebraic integers with discriminants containing fixed prime divisors

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Abstract

It is proved that any algebraic integer a of degree n ≥2whose discriminant is a product of powers of prescribed primes p1, ..., pr has the form\(\alpha = a + \beta p_1^{\upsilon _1 } \ldots p_r ^{\upsilon _r }\), where α, V1, ..., vr are rational integers and β is an integer whose height does not exceed an effectively defined bound depending on max (p1, ..., pr), r, and n.

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Authors and Affiliations

  1. Institute of Mathematics, Academy of Sciences of the Belorussian SSR, USSR

    L. A. Trelina

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  1. L. A. Trelina
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Additional information

Translated from Matematicheskie Zametki, Vol. 21, No. 3, pp. 289–296, March, 1977.

The author would like to thank V. G. Sprindzhuk for his assistance and unfailing interest.

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Trelina, L.A. Algebraic integers with discriminants containing fixed prime divisors. Mathematical Notes of the Academy of Sciences of the USSR 21, 161–165 (1977). https://doi.org/10.1007/BF01106737

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  • DOI: https://doi.org/10.1007/BF01106737

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