Introduction to Number Theory: A Computational Approach

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.

Information and Media Inquiries

May 19, 2026 Publication
Publicity and Interviews: publishing@wolfram.com
Non-Fiction

Contents

• Preface

• What Is Number Theory?
• Integers: The Basics
• Primes and Composites
• Part 1 Exercises

• Prime Factorization
• Multiples and Divisors
• Greatest Common Divisor
• Part 2 Exercises

• Congruences
• Modular Arithmetic
• Chinese Remainder Theorem
• Part 3 Exercises

• Real Number Representations
• Continued Fractions
• Best Rational Approximations
• Part 4 Exercises

• Diophantine Equations
• Linear Diophantine Equations
• Diophantine Equations of Degree 2
• Part 5 Exercises

• Cryptography
• The RSA Algorithm
• Part 6 Exercises

• 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

About the Author

Lusine Sukiasyan is a Kernel Developer in discrete computation at Wolfram. She holds a BSc in informatics and applied mathematics and an MSc in numerical analysis and mathematical modeling, both from Yerevan State University. Her work spans number theory, computational geometry and calculus, and she also contributes to the development of educational content for Wolfram that helps make advanced mathematics more accessible and engaging.

Charles Pooh is the Manager of Discrete Computation at Wolfram, where he works in research and development, focusing on algorithms for Wolfram Language. He holds a postgraduate diploma in mathematics from the International Centre for Theoretical Physics and a PhD in mathematics from the University of Georgia.