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Elementary number theory and its applications I Kenneth H. Rosen. The changes in the sixth edition have been designed to make the book easier to teach.
Table of contents

Prime Numbers. The Distribution of Primes.

Table of Contents

Greatest Common Divisors. The Euclidean Algorithm. The Fundemental Theorem of Arithmetic. Factorization Methods and Fermat Numbers. Linear Diophantine Equations. Introduction to Congruences. Linear Congrences. The Chinese Remainder Theorem. Solving Polynomial Congruences.

Systems of Linear Congruences. Factoring Using the Pollard Rho Method. Applications of Congruences. Divisibility Tests.

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The perpetual Calendar. Round Robin Tournaments. Hashing Functions. Check Digits.

Some Special Congruences. Wilson's Theorem and Fermat's Little Theorem.


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Euler's Theorem. Multiplicative Functions. The Euler Phi-Function. The Sum and Number of Divisors. Perfect Numbers and Mersenne Primes.

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Mobius Inversion. Character Ciphers. Block and Stream Ciphers. Exponentiation Ciphers.


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  • Knapsack Ciphers. Cryptographic Protocols and Applications. Primitive Roots. The Order of an Integer and Primitive Roots. Primitive Roots for Primes. The Existence of Primitive Roots. Index Arithmetic. Universal Exponents. Applications of Primitive Roots and the Order of an Integer. Pseudorandom Numbers. The EIGamal Cryptosystem. An Application to the Splicing of Telephone Cables. Quadratic Residues. Quadratic Residues and nonresidues. The Law of Quadratic Reciprocity.

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