Elementary Number Theory (Series of Books in the Mathematical Sciences)

Title Page......Page 1
Contents......Page 2
Preface......Page 4
Section 1 - Integers......Page 8
Section 2 - Unique Factorization......Page 17
Section 3 - Linear Diophantine Equations......Page 27
Section 4 - Congruences......Page 34
Section 5 - Linear Congruences......Page 41
Section 6 - Fermat's and Wilson's Theorems......Page 49
Section 7 - The Divisors of an Integer......Page 57
Section 8 - Perfect Numbers......Page 64
Section 9 - Euler's Theorem and Function......Page 70
Section 10 - Primitive Roots......Page 80
Section 11 - Quadratic Congruences......Page 90
Section 12 - Quadratic Reciprocity......Page 101
Section 13 - Numbers in Other Bases......Page 113
Section 14 - Duodecimals......Page 121
Section 15 - Decimals......Page 126
Section 16 - Pythagorean Triangles......Page 134
Section 17 - Infinite Descent and Fermat's Conjecture......Page 142
Section 18 - Sums of Two Squares......Page 148
Section 19 - Sums of Four Squares......Page 156
Section 20 - x^2 - Ny^2 = 1......Page 162
Section 21 - Bounds for rr(x)......Page 170
Section 22 - Formulas for Primes......Page 179
Section 23 - Additional Problems......Page 189
Appendix A - Proof by Induction......Page 212
Appendix B - Computer Problems......Page 217
Appendix C - Factor Table for Integers Less Than I0,000......Page 224
References......Page 232
Answers to Selected Exercises......Page 234
Answers to Selected Odd-Numbered Problems......Page 238
Comments on Selected Odd-Numbered Problems......Page 245
Index......Page 254