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| What is Number Theory? | |
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| The Integers | |
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| Numbers and Sequences | |
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| Sums and Products | |
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| Mathematical Induction | |
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| The Fibonacci Numbers | |
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| Integer Representations and Operations | |
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| Representations of Integers | |
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| Computer Operations with Integers | |
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| Complexity of Integer Operations | |
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| Primes and Greatest Common Divisors | |
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| Prime Numbers | |
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| The Distribution of Primes | |
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| Greatest Common Divisors | |
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| The Euclidean Algorithm | |
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| The Fundemental Theorem of Arithmetic | |
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| Factorization Methods and Fermat Numbers | |
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| Linear Diophantine Equations | |
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| Congruences | |
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| Introduction to Congruences | |
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| Linear Congrences | |
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| The Chinese Remainder Theorem | |
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| Solving Polynomial Congruences | |
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| Systems of Linear Congruences | |
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| Factoring Using the Pollard Rho Method | |
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| Applications of Congruences | |
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| Divisibility Tests | |
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| The perpetual Calendar | |
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| Round Robin Tournaments | |
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| Hashing Functions | |
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| Check Digits | |
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| Some Special Congruences | |
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| Wilson's Theorem and Fermat's Little Theorem | |
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| Pseudoprimes | |
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| Euler's Theorem | |
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| Multiplicative Functions | |
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| The Euler Phi-Function | |
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| The Sum and Number of Divisors | |
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| Perfect Numbers and Mersenne Primes | |
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| Mobius Inversion | |
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| Cryptology | |
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| Character Ciphers | |
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| Block and Stream Ciphers | |
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| Exponentiation Ciphers | |
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| Knapsack Ciphers | |
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| Cryptographic Protocols and Applications | |
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| Primitive Roots | |
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| The Order of an Integer and Primitive Roots | |
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| Primitive Roots for Primes | |
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| The Existence of Primitive Roots | |
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| Index Arithmetic | |
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| Primality Tests Using Orders of Integers and Primitive Roots | |
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| Universal Exponents | |
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| Applications of Primitive Roots and the Order of an Integer | |
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| Pseudorandom Numbers | |
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| The EIGamal Cryptosystem | |
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| An Application to the Splicing of Telephone Cables | |
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| Quadratic Residues | |
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| Quadratic Residues and nonresidues | |
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| The Law of Quadratic Reciprocity | |
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| The Jacobi Symbol | |
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| Euler Pseudoprimes | |
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| Zero-Knowledge Proofs | |
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| Decimal Fractions and Continued | |
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| Decimal Fractions | |
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| Finite Continued Fractions | |
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| Infinite Continued Fractions | |
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| Periodic Continued Fractions | |
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| Factoring Using Continued Fractions | |
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| Some Nonlinear Diophantine Equations | |
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| Pythagorean Triples | |
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| Fermat's Last Theorem | |
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| Sums of Squares | |
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| Pell's Equation | |
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| The Gaussian Integers | |
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| Gaussian Primes | |
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| Unique Factorization of Gaussian Integers | |
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| Gaussian Integers and Sums of Squares | |