Description

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This book offers a friendly introduction to number theory from a computational perspective. It starts with the basics, such as divisibility, prime numbers and congruences, and then gradually progresses to more advanced topics like continued fractions, Diophantine equations and cryptography. Abstract ideas are presented in a way that makes them concrete and approachable, with examples that can be explored computationally.

Each chapter is thoughtfully structured to build on the previous ones, and the book is organized into seven key parts, each accompanied by exercises (with solutions) that encourage independent problem solving and verification of results. Readers can download the free interactive ebook version to engage directly with live Wolfram Language code. This book is ideal for students, self-learners and anyone curious about the underlying arithmetic of modern mathematics. Contents

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Preface
Introduction
What Is Number Theory?
Integers: The Basics
Primes and Composites
Part 1 Exercises
Primes and Divisibility
Prime Factorization
Multiples and Divisors
Greatest Common Divisor
Part 2 Exercises
Modular Arithmetic
Congruences
Modular Arithmetic
Chinese Remainder Theorem
Part 3 Exercises
Continued Fractions
Real Number Representations
Continued Fractions
Best Rational Approximations
Part 4 Exercises
Diophantine Equations
Diophantine Equations
Linear Diophantine Equations
Diophantine Equations of Degree 2
Part 5 Exercises
Cryptography
Cryptography
The RSA Algorithm
Part 6 Exercises
Additional Topics
Primality Testing: Miller–Rabin
Factorization: Pollard's Rho
Diophantine Equations: Hilbert's Tenth Problem
The Riemann Zeta Function
Special Numbers
Numeral Systems
Part 7 Exercises Related Topics

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Number Theory