Author(s): Anthony J. Pettofrezzo, Donald R. Byrkit
Publisher: Prentice-Hall
Year: 1970
Language: English
Commentary: Same scan as https://libgen.is/book/index.php?md5=AAF9F62A91E42B674493E2A32FEC445F but binarized from JPG
Pages: 244+xii
City: Englewood Cliffs, NJ
Title
Preface
Contents
1. Preliminary considerations
1.1. Ordered integral domains
1.2. Mathematical induction
1.3. Number bases
1.4. Notations for sums and products
2. Divisibility properties
2.1. Prime and composite numbers
2.2. Some properties of prime numbers
2.3. The greatest common divisor
2.4. The generalized greatest common divisor
2.5. Properties of the greatest common divisor
2.6. Linear Diophantine equations
2.7. The Fundamental Theorem of Arithmetic
2.8. Sum of divisors
2.9. Number of divisors
2.10. Perfect numbers
2.11. Mersenne numbers
2.12. The Euler phi-function
2.13. Properties of the Euler phi-function
2.14. Solution of the equation phi(x) = m
3. The theory of congruences
3.1. Definitions and elementary properties
3.2. Some congruence theorems
3.3. An application of the congruence relation
3.4. Reduced residue systems modulo m
3.5. The theorems of Euler and Fermat
3.6. Linear congruences
3.7. Linear congruences and linear Diophantine equations
3.8. Wilson's theorem
3.9. Linear congruences in two variables
3.10. The Chinese Remainder Theorem
3.11. Quadratic congruences
4. Continued fractions
4.1. Finite continued fractions
4.2. Infinite continued fractions
4.3. Convergents
4.4. Evaluation of convergents
4.5. Convergents as determinants
4.6. Some properties of convergents
4.7. Continued fractions and linear Diophantine equations
4.8. Theorems on infinite continued fractions
4.9. Approximation theorems
4.10. Use of continued fractions in solving quadratic equations
4.11. Periodic continued fractions
4.12. Continued fractions for sqrt(k)
Answers to selected exercises
Chapter 1
Chapter 2
Chapter 3
Chapter 4
List of prime numbers < 10,000
Index
