Elementary Number Theory / Edition 6by Kenneth H. Rosen
Elementary Number Theory, Sixth Edition, blends classical theory with modern applications and is notable for its outstanding exercise sets. A full range of exercises, from basic to challenging, helps readers explore key concepts and push their understanding to new heights. Computational exercises and computer projects are also available. Reflecting many years of… See more details below
Elementary Number Theory, Sixth Edition, blends classical theory with modern applications and is notable for its outstanding exercise sets. A full range of exercises, from basic to challenging, helps readers explore key concepts and push their understanding to new heights. Computational exercises and computer projects are also available. Reflecting many years of professors' feedback, this edition offers new examples, exercises, and applications, while incorporating advancements and discoveries in number theory made in the past few years.
Table of ContentsP. What is Number Theory?
1. The Integers.
Numbers and Sequences.
Sums and Products.
The Fibonacci Numbers.
2. Integer Representations and Operations.
Representations of Integers.
Computer Operations with Integers.
Complexity of Integer Operations.
3. Primes and Greatest Common Divisors.
The Distribution of Primes.
Greatest Common Divisors.
The Euclidean Algorithm.
The Fundemental Theorem of Arithmetic.
Factorization Methods and Fermat Numbers.
Linear Diophantine Equations.
Introduction to Congruences.
The Chinese Remainder Theorem.
Solving Polynomial Congruences.
Systems of Linear Congruences.
Factoring Using the Pollard Rho Method.
5. Applications of Congruences.
The perpetual Calendar.
Round Robin Tournaments.
6. Some Special Congruences.
Wilson's Theorem and Fermat's Little Theorem.
7. Multiplicative Functions.
The Euler Phi-Function.
The Sum and Number of Divisors.
Perfect Numbers and Mersenne Primes.
Block and Stream Ciphers.
Cryptographic Protocols and Applications.
9. Primitive Roots.
The Order of an Integer and Primitive Roots.
Primitive Roots for Primes.
The Existence of Primitive Roots.
Primality Tests Using Orders of Integers and Primitive Roots.
10. Applications of Primitive Roots and the Order of an Integer.
The EIGamal Cryptosystem.
An Application to the Splicing of Telephone Cables.
11. Quadratic Residues.
Quadratic Residues and nonresidues.
The Law of Quadratic Reciprocity.
The Jacobi Symbol.
12. Decimal Fractions and Continued.
Finite Continued Fractions.
Infinite Continued Fractions.
Periodic Continued Fractions.
Factoring Using Continued Fractions.
13. Some Nonlinear Diophantine Equations.
Fermat's Last Theorem.
Sums of Squares.
14. The Gaussian Integers.
Unique Factorization of Gaussian Integers.
Gaussian Integers and Sums of Squares.
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