Enchantment of Numbers

Inbunden, Engelska, 2025

Av Eric L. F. Roettger, Hugh C. Williams

2 349 kr

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Here, we re-examine most of the key topics Beiler covered, while introducing fresh updates and insights rooted in computational number theory.The authors aim to present efficient computer algorithms to tackle various problems that arise in the theory of numbers, providing a deeper and more modern perspective on these timeless puzzles.

Produktinformation

Utgivningsdatum2025-07-03
Mått155 x 235 x 25 mm
Vikt680 g
FormatInbunden
SpråkEngelska
SerieCMS/CAIMS Books in Mathematics
Antal sidor324
FörlagSpringer International Publishing AG
ISBN9783031765674

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Eric completed his undergraduate work in 2002 from the University of Regina receiving bachelor degrees in both mathematics and computer science. He remained in Regina for his masters work, doing research on Lucas functions under the supervision of Dr. Richard McIntosh. He went on to complete his doctorate at the University of Calgary, with a dissertation titled, A Cubic Extension of the Lucas Functions, under the supervision of Dr. Hugh Williams and Dr. Siguna Muller.Eric is an Associate Professor cross appointed between the departments of General Education and Mathematics and Computing. Eric works in the area of elementary number theory, in particular with Lucas functions and other divisibility sequences.Dr. Hugh Williams is internationally recognized as an expert in computational number theory and its applications to cryptography. He has authored over 150 refereed journal papers, 30 refereed conference papers and 20 books or book chapters. After a university career of 46 years, he was appointed Professor Emeritus in Mathematics and Statistics at the University of Calgary.

Introduction.- Division, factors, primes, congruences, gcd, etc.- Representations of Integers.- Integer Powers.- The Binomial Congruence.- The Binomial Coeﬃcients.- Public-Key Cryptography.- Fibonacci and Lucas Numbers.- Sociable Numbers.- Lucas and Lehmer Sequences.- Primality.- Prime Curios.- Linear Recurrence Sequences.- Simple Continued Fractions.- Integer Factorization.- Sieve Devices.- Simple Continued Fraction of √𝑫.- Formulas for Primes.- The Pell Equation.- Some Diophantine Equations.- Conclusion.