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redmond d number theory introduction 1996

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Textbook in PDF format This reference text provides a detailed introduction to number theory--demonstrating how other areas of mathematics enter into the study of the properties of natural numbers. Preface Historical Introduction Primes and Divisibility Introduction Divisibility Prime numbers Unique factorization Some factorization methods, I Additional problems Congruences Congruences The Euler phi function Congruences of the first degree The Chinese remainder theorem Polynomial congruences Prime power moduli Prime moduli Primitive roots Indices and binomial and exponential congruences An application to cryptography Pseudoprimes Additional problems Quadratic Residues Introduction Quadratic residues The law of quadratic reciprocity The Jacobi symbol The Kronecker symbol The solution of x^2 = D (mod m) Additional problems Approximation of Real Numbers Introduction Farey fractions Approximation by rationals, I Continued fractions Periodic continued fractions Approximation by rationals, II Some factorization methods, II Equivalent numbers Decimal representation Additional problems Diophantine Equations, I Introduction Pythagorean triangles Related quadratic equations The equation ax^2 + by^2 + cz^2 = 0 Additional problems Diophantine Equations, II Introduction Linear equations Sums of two squares Sums of four squares Sums of other numbers of squares Binary quadratic forms The equation x^2 - D y^2 = N A Pythagorean triangle problem The equation ax^2 + bxy + cy^2 + dx + ey + f = 0 Waring's problem Additional problems Arithmetic Functions Introduction Dirichlet convolution Multiplicative functions Sum of divisors Number of divisors Euler's function Characters Trigonometrical sums Additive functions Linear recursion Additional problems The Average Order of Arithmetic Functions Introduction The greatest integer function Preliminaries Sum of divisors function The number of divisors functions Euler's function Lattice point problems Additional problems Prime Number Theory Introduction Bertrand's postulate and Chebychev's theorem The prime number theorem Primes in arithmetic progressions Order of magnitude of multiplicative functions Summatory functions of additive functions Additional problems An Introduction To Algebraic Number Theory Introduction General considerations Quadratic number fields Applications to Diophantine equations Concluding remarks Additional problems Tables Bibliography Index

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redmond d number theory introduction 1996