360 Problems for Mathematical Contests

This book is intended to help students preparing for all rounds of Mathematical Olympiads or any other significant mathematics contest. Teachers will also find this work useful in training young talented students. Our experience as contestants was a great asset in preparing this book. To this we added our vast personal experience from the other side of the "barricade", as creators of problems and members of numerous contest committees.The book is organized in six chapters: algebra, number theory, geometry, trigonometry, analysis and comprehensive problems. In addition, other fields of mathematics found their place in this book, for example, combinatorial problems can be found in the last chapter, and problems involving complex numbers are included in the trigonometry section. Moreover, in all chapters of this book the serious reader can find numerous challenging inequality problems. All featured problems are interesting, with an increased level of difficulty; some of them are real gems that will give great satisfaction to any math lover attempting to solve or even extend them. Cuprins FOREWORDFROM THE AUTHORSChapter 1. ALGEBRAProblemsSolutionsChapter 2. NUMBER THEORYProblemsSolutionsChapter 3. GEOMETRYProblemsSolutionsChapter 4. TRIGONOMETRYProblemsSolutionsChapter 5. MATHEMATICAL ANALYSISProblemsSolutionsChapter 6. COMPREHENSIVE PROBLEMSProblemsSolutions