This is the first English translation of the revised edition of this important mod-ern book on number theory. Clear and detailed in its exposition, most of it can be understood by readers who have no background in advanced mathematics; only a small part requires a working knowledge of calculus. One of the most valuable characteristics of this book is its stress on learning number theory by means of demonstrations and problems. More than 200 problems, with full solu-tions, are presented in the text, while more than 100 numerical exercises afford further practice. Some of these exercises deal with estimation of trigonometric sums, and are especially valuable as introductions to more advanced studies.
Partial contents: Divisibility Theory; greatest common divisor, Euclid's algo-rithm, fundamental properties of fractions, unique factorization theorem, etc. Important Number-Theoretic Functions; the factorization of n!, with various functions, and general properties of multiplicative functions. Congruences; basic properties, reduced residue systems, theorems of Fermat, Euler. Congruences in One Unknown; continued fraction solution of linear congru-ence, congruences with composite and prime power moduli, Wilson's theorem. Congruences of the Second Degree; Legendre, Jacobi symbols, solution of the congruence x2 = a (mod m). Primitive Roots and Indices; determination of all moduli having primitive roots and corresponding theory of indices. |
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