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Русский
Olympiad
Links: 2
Entries: 22
Прасолов В.В.
Орыс тілінде
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22
Preface
Other
Page 2
1. Conjugate numbers
Theory
Page 2
2. Rational parametrization of a circle
Theory
Page 4
3. Sums of squares of polynomials
Theory
Page 6
4. Representation of numbers as a sum of two squares
Theory
Page 8
5. Can every knot be untied?
Theory
Page 9
6. Construction of a regular 17-gon
Theory
Page 11
7. Solving cubic and quartic equations
Theory
Page 14
8. Intersection points of diagonals of regular polygons
Theory
Page 16
9. Cubic equations related to a triangle
Theory
Page 19
10. Markov equation
Theory
Page 21
11. Integer-valued polynomials
Theory
Page 22
12. Brocard points
Theory
Page 23
13. Chebyshev polynomials
Theory
Page 27
14. Averaging method and geometric inequalities
Theory
Page 29
15. Chromatic polynomial of a graph
Theory
Page 33
16. Diophantine equations for polynomials
Theory
Page 35
17. Pascal lines
Theory
Page 37
18. The butterfly theorem and the two-butterfly theorem
Theory
Page 40
19. Van der Waerden's theorem on arithmetic progressions
Theory
Page 41
20. Isogonally conjugate points
Theory
Page 44
21. Cubic curves related to a triangle
Theory
Page 48
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