Tattersall - Elementary Number Theory in Nine Chapters (2e)

Elementary Number Theory in Nine Chapters (2e),

by James J. Tattersall,

Cambridge Univ Press, 2005.

443 pages.

Contents
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1 The intriguing natural numbers
1.1 Polygonal numbers
1.2 Sequences of natural numbers
1.3 The principle of mathematical induction
1.4 Miscellaneous exercises
1.5 Supplementary exercises

2 Divisibility
2.1 The division algorithm
2.2 The greatest common divisor
2.3 The Euclidean algorithm
2.4 Pythagorean triples
2.5 Miscellaneous exercises
2.6 Supplementary exercises

3 Prime numbers
3.1 Euclid on primes
3.2 Number theoretic functions
3.3 Multiplicative functions
3.4 Factoring
3.5 The greatest integer function
3.6 Primes revisited
3.7 Miscellaneous exercises
3.8 Supplementary exercises

4 Perfect and amicable numbers
4.1 Perfect numbers
4.2 Fermat numbers
4.3 Amicable numbers
4.4 Perfect-type numbers
4.5 Supplementary exercises

5 Modular arithmetic
5.1 Congruence
5.2 Divisibility criteria
5.3 EulerΓÇÖs phi-function
5.4 Conditional linear congruences
5.5 Miscellaneous exercises
5.6 Supplementary exercises

6 Congruences of higher degree
6.1 Polynomial congruences
6.2 Quadratic congruences
6.3 Primitive roots
6.4 Miscellaneous exercises
6.5 Supplementary exercises

7 Cryptology
7.1 Monoalphabetic ciphers
7.2 Polyalphabetic ciphers
7.3 Knapsack and block ciphers
7.4 Exponential ciphers
7.5 Supplementary exercises

8 Representations
8.1 Sums of squares
8.2 PellΓÇÖs equation
8.3 Binary quadratic forms
8.4 Finite continued fractions
8.5 In?nite continued fractions
8.6 p -Adic analysis
8.7 Supplementary exercises

9 Partitions
9.1 Generating functions
9.2 Partitions
9.3 Pentagonal Number Theorem
9.4 Supplementary exercises

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