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+-------- Thread: The Enchantment of Numbers [Roettger] (/showthread.php?tid=2372)
The Enchantment of Numbers [Roettger] - mklabgr - 10-28-2026
The Enchantment of Numbers
In their book The Enchantment of Numbers, mathematicians Eric L. F. Roettger and Hugh C. Williams explore the fascinating world of number theory, combining classical mathematical puzzles with modern computational techniques. Inspired by Albert H. Beiler’s celebrated book on recreational number theory, the authors revisit many traditional topics while updating them with new insights and efficient computer algorithms. Their aim is to reveal the beauty, creativity, and intellectual excitement hidden within the properties of integers.
The book consists of 21 chapters covering a wide range of subjects, including prime numbers, divisibility, congruences, integer representations, binomial coefficients, Fibonacci and Lucas numbers, continued fractions, and Diophantine equations. It also explores primality testing, integer factorization, sieve methods, and public-key cryptography, demonstrating how abstract mathematical ideas connect with computational problems and applications. Throughout the book, readers encounter important results, algorithms, examples, and mathematical problems that encourage further investigation.
The central message is that number theory is not merely an abstract branch of mathematics, but a living subject full of patterns, puzzles, and practical applications. By combining historical ideas with computational approaches, the authors show how modern technology can deepen our understanding of mathematical problems without diminishing their elegance. With exercises, selected solutions, and references for further reading, the book is suitable for mathematically curious readers and students with an interest in exploring the rich relationships between numbers.
Read the book description on Springer.