02179nam a22002537a 4500 55796 55796 20191022140607.0 191022b ||||| |||| 00| 0 eng d 9781470454814 512.7 EDW Edwards, Harold M. Higher arithmetic : an algorithmic introduction to number theory / Harold M Edwards Providence, R.I. : American Mathematical Society, ©2008 xii, 210 pages : illustrations ; 22 cm. Student mathematical library, v. 45. 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. "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. Mathematics Algebra Number theory. Zahlentheorie. Talteori. Edwards, Harold M. MDL 0 0 ddc 0 0 MDL SNUL 2019-10-22 0 512.7 EDW M033 2019-10-22 00:00:00 2019-10-22 MDL