2011 JBMO Problems
Let be positive real numbers such that . Prove that:
Find all primes such that there exist positive integers that satisfy .
Let be a positive integer. Equilateral triangle ABC is divided into smaller congruent equilateral triangles (with sides parallel to its sides). Let be the number of rhombuses that contain two small equilateral triangles and the number of rhombuses that contain eight small equilateral triangles. Find the difference in terms of .
Let be a convex quadrilateral and points and on sides such that
If is the area of show that
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