We assume that readers are already familiar with basic number theory concepts, such as divisibility and greatest common divisor, but this is not a strict prerequisite – a keen student can begin right away. This volume is to introduce readers to further concepts in number theory, and then show how they can be applied to solve problems. It is meant to serve more as a problem-manual rather than a formal textbook, and proofs of theorems are sometimes replaced by well-chosen examples. And, all solutions are worked out in detail, as they would have to be on a written test. The design of this book is to actually attempt the reader to solve the problems in this booklet, rather than go straight to the solutions. For this purpose, problems are given at the end of each chapter to allow the reader to try to solve them. Many of the problems allow for different approaches, so you may find a solution that is different from ours which is still correct. We hope you enjoy reading and learning about number theory and the problem-solving process and I welcome any suggestions. Happy solving!
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