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A Comprehensive Course in Number Theory by Alan Baker

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Introduction

Gauss and Number Theory

Without doubt the theory of numbers was Gauss’ favourite subject. Indeed, in a much quoted dictum, he asserted that Mathematics is the Queen of the Sciences and the Theory of Numbers is the Queen of Mathematics. Moreover, in the introduction to Eisenstein’s Mathematische Abhandlungen, Gauss wrote:

The Higher Arithmetic presents us with an inexhaustible storehouse of interesting truths – of truths, too, which are not isolated but stand in the closest relation to one another, and between which, with each successive advance of the science, we continually discover new and sometimes wholly unexpected points of contact. A great part of the theories of Arithmetic derive an additional charm from the peculiarity ...

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