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Unsolved Problems in Number Theory (Texts in Applied Mathematics) (v. 1)

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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.

Another of my 10 favorite books. A constant source of inspiration