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This document contains a summary of problems from the 2005 Balkan Mathematics Olympiad: 1) Prove that a triangle formed by intersecting lines from an inscribed circle is equilateral if and only if one angle of the original triangle is 60 degrees. 2) Find all prime numbers p such that p^2 - p + 1 is a perfect cube. 3) Prove an inequality involving sums of powers of three positive real numbers and find when equality occurs. 4) Determine the maximum possible number of elements in a set where no two elem

Author

Jhefferson Lopez

Language

EN