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andreescu t number theory concepts problems 2017

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Textbook in PDF format Exercises are in mathematics like a vitalizer: they strengthen and train the elasticity of the mind, teach a variety of successful methods for approaching specific problems, and enrich the professional culture with interesting questions and results. For a good treatment of a theory, examples and exercises are the art of presenting concrete applications, reflecting the strength and potential of the theoretical results. A strong theory explained only by simple exercise often may reduce the motivation of the reader. At the other end, there is a wide reserve of problems and exercises of elementary looking nature, but requiring vivid mind and familiarity with a good bag of tricks, problems of styles which were much developed by the interest that mathematical competition attracted worldwide in the last 50 years. These problems can only loosely be ordered into applications of individual theories of mathematics, their flavor and interest relaying in the way they combine different areas of knowledge with astute techniques of solving. Often, not always, the problems addressed have some deeper interest of their own and can very well be encountered as intermediate steps in the development of mathematical theories. From this perspective, a good culture of problems can be to a mathematician as helpful, as the familiarity with classical situations in chess matches, to a professional chess player: they develop the aptitude to recognize, formulate and solve individual problems that may play a crucial role in theories and proofs of deeper significance. The book at hand is a powerful collection of competition problems with number theoretical flavor. They are generally grouped according to common aspects, related to topics like Diaisibility, GOD and LCM, decomposition of polynomials, Congruences and p-adz'c valuations, etc. And these aspects can be found in the problems discussed in the respective chapter — beware though to expect much connection to the typical questions one would find in an introductory textbook to number theory, at the chapters with the same name. The problems here are innovative findings and questions, and the connection is more often given by the methods used for the solution, than by the very nature of the problem

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Andreescu T. Number Theory. Concepts and Problems 2017.pdf 40.7 MB

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andreescu t number theory concepts problems 2017

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