MATHEMATICAL OLYMPIAD CHALLENGES

published by Birkhauser

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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

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

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 unknowns as exponents
3.7. Numerical functions
3.8. Invariants
3.9. Pell equations
3.10. Prime numbers and binomial coefficients

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