Titlebook: Classical Theory of Algebraic Numbers; Paulo Ribenboim Textbook 2001Latest edition Springer Science+Business Media New York 2001 algebra.a

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https://doi.org/10.1007/978-3-031-01750-6In this chapter we investigate the following question. Let . > 1 and let a be an integer relatively prime to .. When is the residue class ā a square in the multiplicative group P(.)? In other words, when does there exist an integer . such that .. ≡ a (mod .)?

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Academic Assessment and InstrumentationIn this chapter we study the discriminant. A method of “Geometry of Numbers” is used to provide sharper estimates for the discriminant.

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Academic Assessment and InstrumentationAs we have said, two elements of a domain are associated precisely when they generate the same ideal. Thus, by considering ideals, we ignore the units. However, it will become apparent that a number of arithmetic properties are intimately tied up with the units of the ring of integers . of the algebraic number field ..

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https://doi.org/10.1007/978-1-4613-8345-1For the convenience of the reader, this chapter is devoted to the detailed presentation of algebraic results, which will be needed in the sequel.

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