5th Junior Balkan Mathematical Olympiad Problems 2001

1.  Find all positive integers a, b, c such that a3 + b3 + c3 = 2001. 2.  ABC is a triangle with ∠C = 90o and CA ≠ CB. CH is an altitude and CL is an angle bisector. Show that for X ≠ C on the line CL, we have ∠XAC ≠ ∠XBC. Show that for Y ≠ C on the line CH we have ∠YAC ≠ ∠YBC.