Number theory is the most enigmatic of disciplines, in that the problems are so easy to state and understand and yet so hard to resolve. Furthermore, when solved, the proofs are sometimes surprisingly easy. In this collection, Guy has put together a truly fascinating survey of what is currently (un)known about numbers. Each page is an excursion into the extensive labyrinths carved out by numbers. Approximately once a month, I scan it looking for new avenues to explore. Invariably, I see something, sketch out some possible proof routes and then end in frustration. A typical result of working in number theory. Whether you are an amateur or professional, if you have an interest in number theory, you will like this book. Perhaps you will be able to make some progress towards resolving some of these problems. It is certainly possible, as no field has had more positive contributions from amateurs than number theory. Even Fermat fit the definition of an amateur.
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Charles Ashbacher (CharlesAshbacher)
Charlie Ashbacher is a compulsive reader and writer about many subjects. His prime areas of expertise are in mathematics and computers where he has taught every course in the mathematics and computer … more
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This book contains discussions of hundreds of open questions in number theory, organized into 185 different topics. They represent numerous aspects of number theory and are organized into six categories: prime numbers, divisibility, additive number theory, Diophantine equations, sequences of integers, and miscellaneous. To prevent repetition of earlier efforts or duplication of previously known results, an extensive and up-to-date collection of references follows each problem. In the second edition, extensive new material has been added, and corrections have been included throughout the book. This volume is an invaluable supplement to any course in number theory.