Problems for the Mathematical Olympiads

This book consists of a number of math problems, all of which are meant primarily as preparation for competitions such as the International Mathematical Olympiad. They are therefore of IMO level, and require only elementary notions of math; however, since the International Mathematical Olympiad is perhaps the most difficult exam in elementary mathematics, any participant should have with him a good knowledge and grasp of what he is dealing with. This book is not meant to teach elementary math at an IMO level, but to help a prospective participant train and enhance his understanding of these concepts.The second this that is important about this book is the solutions. Any good participant at an IMO needs to know not so much theory as tricks to be employed in elementary problems. It is far less useful as far as IMO's are concerned (and far more difficult) for a student to learn multivariable calculus and Lagrange multipliers than to know how to apply geometrical inversion. That is why I emphasize on all these methods, lemmas and propositions in my solutions, and I have often sacrificed succinctness of a proof to the educational value of presenting one of these methods. Cuprins FOREWORDI. ProblemsChapter 1. GEOMETRYChapter 2. NUMBER THEORYChapter 3. COMBINATORICSChapter 4. ALGEBRAII. SolutionsChapter 1. GEOMETRYChapter 2. NUMBER THEORYChapter 3. COMBINATORICSChapter 4. ALGEBRAIII. APPENDIX 1: USEFUL FACTSIV. APPENDIX 2: SOURCES OF PROBLEMS