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Foreword

Preface

Part I Problems

1 Geometry and Trigonometry

1.1 A Property of Equilateral Triangles

1.2 Cyclic Quadrilaterals

1.3 Power of a Point

1.4 Dissections of Polygonal Surfaces

1.5 Regular Polygons

1.6 Geometric Constructions and Transformations

1.7 Problems with Physical Flavor

1.8 Tetrahedra Inscribed in Parallelepipeds

1.9 Telescopic Sums and Products in Trigonometry

1.10 Trigonometric Substitutions

2 Algebra and Analysis

2.1 No Square Is Negative

2.2 Look at the Endpoints

2.3 Telescopic Sums and Products in Algebra

2.4 On an Algebraic Identity

2.5 Systems of Equations

2.6 Periodicity

2.7 The Abel Summation Formula

2.8 x+1/x

2.9 Matrices

2.10 The Mean Value Theorem

3 Number Theory and Combinatorics

3.1 Arrange in Order

3.2 Squares and Cubes

3.3 Repunits

3.4 Digits of Numbers

3.5 Residues

3.6 Diophantine Equations with the Unknowns as Exponents

3.7 Numerical Functions

3.8 Invariants

3.9 Pell Equations

3.10 Prime Numbers and Binomial Coefficients

Part II Solutions

4 Geometry and Trigonometry

5 Algebra and Analysis

6 Number Theory and Combinatorics

Appendix: Definitions and Notation