Book contents
- Frontmatter
- Introduction
- Contents
- 1 Greatest Common Divisors
- 2 Unique Factorization
- 3 Linear Diophantine Equations
- 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 Roots and Orders
- 15 Decimals
- 16 Quadratic Congruences
- 17 Gauss's Lemma
- 18 The Quadratic Reciprocity Theorem
- 19 The Jacobi Symbol
- 20 Pythagorean Triangles
- 21 x4 + y4 ≠ z4
- 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 π(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
This chapter is part of a book that is no longer available to purchase from Cambridge Core
4 - Congruences
Book contents
- Frontmatter
- Introduction
- Contents
- 1 Greatest Common Divisors
- 2 Unique Factorization
- 3 Linear Diophantine Equations
- 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 Roots and Orders
- 15 Decimals
- 16 Quadratic Congruences
- 17 Gauss's Lemma
- 18 The Quadratic Reciprocity Theorem
- 19 The Jacobi Symbol
- 20 Pythagorean Triangles
- 21 x4 + y4 ≠ z4
- 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 π(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
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- A Guide to Elementary Number Theory , pp. 13 - 16Publisher: Mathematical Association of AmericaPrint publication year: 2009