Elementary Number Theory

Credits Preface 0 What is Number Theory? 1 Divisibility 1.1 The GCD and LCM 1.2 The Division Algorithm 1.3 The Euclidean Algorithm 1.4 Linear Combinations 1.5 Congruences 1.6 Mathematical Induction 2 Prime Numbers 2.1 Prime Factorization 2.2 The Fundamental Theorem of Arithmetic 2.3 The Importance of Unique Factorization 2.4 Prime Power Factorizations 2.5 A Set of Primes is Infinite 2.6 A Formula for (n) 3 Numerical Functions 3.1 The Sum of the Divisors 3.2 Multiplicative Functions 3.3 Perfect Numbers 3.4 Mersenne and Fermat Numbers 3.5 The Euler Phi Function 4 The Algebra of Congruence Classes 4.1 Solving Linear Congruences 4.2 The Chinese Remainder Theorem 4.3 The Theorems of Fermat and Euler 4.4 Primality Testing 4.5 Public-Key Cryptography 5 Congruences of Higher Degree 5.1 Polynomial Congruences 5.2 Congruences with Prime Power Moduli 5.3 Quadratic Residues 5.4 Quadratic Reciprocity 5.5 Flipping a Coin over the Telephone 6 The Number Theory of the Reals 6.1 Rational and Irrational Numbers 6.2 Finite Continued Fractions 6.3 Infinite Continued Fractions 6.4 Decimal Representation 6.5 Lagrange's Theorem and Primitive Roots 7 Diophantine Equations 7.1 Pythagorean Triples 7.2 Sums of Two Squares 7.3 Sums of Four Squares 7.4 Sums of Fourth Powers 7.5 Pell's Equation Bibliography Answers to Odd-Numbered Problems IndexVanden Eynden, Charles L. is the author of 'Elementary Number Theory', published 2001 under ISBN 9780072325713 and ISBN 0072325712.