Introduction -- Contents -- 1 Greatest CommonDivisors -- 2 Unique Factorization -- 3 Linear DiophantineEquations -- 4 Congruences -- 5 Linear Congruences -- 6 The Chinese Remainder Theorem -- 7 Fermat's Theorem -- 8 Wilson's Theorem -- 9 The Number of Divisors of an Integer -- 10 The Sum of the Divisors of an Integer -- 11 Amicable Numbers -- 12 Perfect Numbers -- 13 Euler's Theorem and Function -- 14 Primitive Rootsand Orders -- 15 Decimals -- 16 Quadratic Congruences -- 17 Gauss's Lemma -- 18 The Quadratic Reciprocity Theorem -- 19 The Jacobi Symbol -- 20 Pythagorean Triangles -- 21 x^4 + y*4 not= z^4 -- 22 Sums of Two Squares -- 23 Sums of Three Squares -- 24 Sums of Four Squares -- 25 Waring's Problem -- 26 Pell's Equation -- 27 Continued Fractions -- 28 Multigrades -- 29 Carmichael Numbers -- 30 Sophie Germain Primes -- 31 The Group of Multiplicative Functions -- 32 Bounds for pi(x) -- 33 The Sum of the Reciprocals of the Primes -- 34 The Riemann Hypothesis -- 35 The Prime Number Theorem -- 36 The abc Conjecture -- 37 Factorization and Testing for Primes -- 38 Algebraic and Transcendental Numbers -- 39 Unsolved Problems -- Index -- About the Author.