2007 JBMO Problems
Let be positive real number such that . Prove that the equation has no real solution.
Let be a convex quadrilateral with , and . The diagonals and intersect at point . Determine the measure of .
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.
Prove that if is a prime number, then is not a perfect square.
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