University of Calgary

Fundamental Number Theory with Applications


My tenth book is the second edition of Fundamental Number Theory with Applications, the first edition of which was published in 1998. This second edition is a radical rewriting of the first edition. Indeed, virtually all advanced material has been removed and there has been an addition of new material such as combinatorial number theory, partitions, and generating functions. There is also an expanded and more involved discussion of random number generation, more applications to cryptology, primality testing, and factoring. As well there is an expanded coverage of Diophantine equations from a more elementary point of view. This includes a section for Legendre''s Theorem on the equation ax^2+by^2+cz^2=0 and an expanded view of Bachet''s equation y^2=x^3+k. Moreover, the coverage of sums of two, three, and four squares has been revised completely. This edition concentrates on criteria for representation and more on the total number of primitive representations where the extensive coverage of the total number of imprimitive representations in the first edition has been deleted. On the topic of sums of two squares, applications from continued fraction theory which was not covered in the first edition, are discussed in detail. Sums of cubes is given a separate section, also not covered in the first edition. See below for the Table of Contents of the second edition. Thus, now the text is truly "fundamental".


Chapman&Hall/Crc Press, Taylor and Francis Group
Boca Raton, London, New York
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