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OverviewAlthough number theorists have sometimes shunned and even disparaged computation in the past, today's applications of number theory to cryptography and computer security demand vast arithmetical computations. These demands have shifted the focus of studies in number theory and have changed attitudes toward computation itself. Full Product DetailsAuthor: Harold M. EdwardsPublisher: American Mathematical Society Imprint: American Mathematical Society Edition: illustrated edition Volume: No. 45 Weight: 0.276kg ISBN: 9780821844397ISBN 10: 0821844393 Pages: 210 Publication Date: 30 March 2008 Audience: College/higher education , Professional and scholarly , Postgraduate, Research & Scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsNumbers The problem $A\square + B = \square$ Congruences Double congruences and the Euclidean algorithm The augmented Euclidean algorithm Simultaneous congruences The fundamental theorem of arithmetic Exponentiation and orders Euler's $\phi$-function Finding the order of $a\bmod c$ Primality testing The RSA cipher system Primitive roots $\bmod\p$ Polynomials Tables of indices $\bmod\ p$ Brahmagupta's formula and hypernumbers Modules of hypernumbers A canonical form for modules of hypernumbers Solution of $A\square + B = \square$ Proof of the theorem of Chapter 19 Euler's remarkable discovery Stable modules Equivalence of modules Signatures of equivalence classes The main theorem Which modules become principal when squared? The possible signatures for certain values of $A$ The law of quadratic reciprocity Proof of the Main Theorem The theory of binary quadratic forms Composition of binary quadratic forms Cycles of stable modules Answers to exercises Bibliography Index.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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