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Definitions, Solved and Unsolved Problems, Conjectures, and Theorems in Number Theory and Geometry

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Florentin Smarandache is one of the most prolific creators of mathematics problems in the world today. I have written three books on his problems and am currently writing a fourth. Many others also regularly work on the problems he has posed, which are collectively called Smarandache Notions. However, this still leaves a tremendous number of problems unexamined and unresolved.
Smarandache is best known for presenting problems rather than resolving them and that is also the case in this book. Basically, it is a collection of problems where each is listed and followed by a short blurb and references to what work has been done. While some of the problems have been solved, most are very difficult and may never be resolved. For many, a resolution would lead to a great deal of fame, as it would require some extremely original mathematics. No less a mathematical powerhouse than the late Pal Erdos has stated that some of these problems may never be resolved.
Mathematicians live, die and build their careers by finding and resolving problems. Thus collection contains many that are hard, perhaps impossible, but certainly worth examining if you are looking for new challenges.