2007 JBMO Problems
Problem 1
Let be positive real number such that . Prove that the equation has no real solution.
Problem 2
Let be a convex quadrilateral with , and . The diagonals and intersect at point . Determine the measure of .
Problem 3
Given are points in the plane, no three of them belonging to a same line. Each of these points is colored using one of four given colors. Prove that there is a color and at least scalene triangles with vertices of that color.
Problem 4
Prove that if is a prime number, then is not a perfect square.
See Also
2007 JBMO (Problems • Resources) | ||
Preceded by 2006 JBMO |
Followed by 2008 JBMO | |
1 • 2 • 3 • 4 | ||
All JBMO Problems and Solutions |