Titlebook: A Concrete Introduction to Higher Algebra; Lindsay N. Childs Textbook 19952nd edition Springer Science+Business Media New York 1995 algebr

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Textbook 19952nd edition from a set of notes written in the 1970sfor a sophomore-junior level course at the University at Albany entitled "Classical Algebra." The objective of the course, and the book, is to give students enough experience in the algebraic theory of the integers and polynomials to appre- ciate the basic co

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0172-6056 ok emerged from a set of notes written in the 1970sfor a sophomore-junior level course at the University at Albany entitled "Classical Algebra." The objective of the course, and the book, is to give students enough experience in the algebraic theory of the integers and polynomials to appre- ciate th

痛打

Aesthetik auf realistischer Grundlagepts of congruences and congruence classes, and analogues of Fermat’s theorem and the Chinese remainder theorem. When the theory for polynomials is combined wih the theory for integers, what comes out in Chapters 28 and 30 is the theory of finite fields.

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保守

A Concrete Introduction to Higher Algebra978-1-4419-8702-0Series ISSN 0172-6056 Series E-ISSN 2197-5604

原來

Gaia or Knowledge without Spheresvailable in modern computational number theory. In this chapter we look at Euclid’s algorithm and its immediate consequences, analyze its speed, and, as an interesting aside, discuss a speculative connection between Euclid’s algorithm and classical Greek proofs that √n is irrational when . is not a square.

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該得

https://doi.org/10.1007/978-1-349-15461-6 that if . is any subgroup of ., then the number of elements of . is a divisor of the number of elements of .. This famous result is called Lagrange’s theorem. Euler’s and Fermat’s theorems are easy consequences of Lagrange’s theorem.

山頂可休息

Unity and Dynamism: The Interplay, see in the exercises. But suitably reinterpreted, it is a powerful tool for helping us understand how numbers relate in different moduli. As a first application, it yields a nice proof of a formula for Euler’s phi-function.