: an algorithmic introduction to number theory Edwards, Harold M. creator Edwards, Harold M. text Providence, R.I : American Mathematical Society ©2008 monographic eng

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xii, 210 pages : illustrations ; 22 cm. "Higher Arithmetic explains number theory in a way that gives deductive reasoning, including algorithms and computations, the central role. Hands-on experience with the application of algorithms to computational examples enables students to master the fundamental ideas of basic number theory. This is a worthwhile goal for any student of mathematics and an essential one for students interested in the modern applications of number theory."--Jacket. Numbers -- The problem A + B = -- Congruences -- Double congruences and the Euclidean algorithm -- The augmented Euclidean algorithm -- Simultaneous congruences -- The fundamental theorem of arithmetic -- Exponentiation and orders -- Euler's 0-funtion -- Finding the order of a mod c -- Primality testing -- The RSA Cipher system -- Primitive roots mod p -- Polynomials -- Tables of indices mod p. Brahmagupta's Formule and hypernumbers -- Modules of hypernumbers -- A canonical form for modules of hypernumbers -- Solution of A + B = -- Proof of the theorem of chapter 19 -- Euler's remarkable discovery -- Stable modules -- Equivalence of modules -- Signatures of equivalence classes -- The Main theorem -- Modules that 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. / Harold M Edwards Mathematics Algebra Number theory Zahlentheorie Talteori 512.7 EDW 9781470454814 191022 20191022140607.0