Transcription of Elementary Number Theory - 2nd Ed.
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Elementary Number Theory - 2nd Ed.
Elementary Number Theory Second Edition V nderwood Dudley DePauw University rn w. H. FREEMAN AND COMPANY New York Section 1 Section 2 Section 3 Section 4 Section 5 Section 6 Section 7 Section 8 Section 9 Section 10 Section 11 Preface vii Integers 1 Contents Unique Factorization 10 Linear Diophantine Equations 20 Congruences 27 Linear Congruences 34 Fermat's and Wilson's Theorems 42 The Divisors of an Integer 50 Perfect Numbers 57. Euler's Theorem and Function 63 Primitive Roots 73 Quadratic Congruences 83 v vi Contents Section 12 Section 13 Section 14 Section 15 Section 16 Section 17 Section 18 Section 19 Section 20 Section 21 Section 22 Section 23 Appendix A Appendix B Appendix C Quadratic Reciprocity 94 Numbers in Other Bases 106 Duodecimals 114 Decimals 119 Pythagorean Triangles 127 Infinite Descent and Fermat's Conjecture 135 Sums of Tw o Squares 141 Sums of Four Squares 149 Xl -Ny::! = 1 155 Bounds for mx) 163 Formulas for Primes 172 Additional Problems 182 Proof by Induction 205 Computer Problems 210 Factor Table for Integers Less Than 10,000 217 References 225 Answers to Selected Exercises 227 Answers to Selected Odd-Numbered Problems 231 Comments on Selected Odd-Numbered Problems 238 Index 247 Preface Mathematics exists mainly to give us power and control over the phys ical world, but it has always been so fascinating that it was studied for its own sake.
A course in number theory can do several things for a student. It can acquaint him or her with ideas no student of mathematics should be ignorant of. More important, it is an example of the mathematical style of thinking-problem, deduction, solution-in a system where the ...
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