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Wednesday, October 13, 2010
25th Eötvös Competition Problems 1918
1. AC is the long diagonal of a parallelogram ABCD. The perpendiculars from C meet the lines AB and AD at P and Q respectively. Show that AC2 = AB·AP + AD·AQ. 2. Find three distinct positive integers a, b, c such that 1/a + 1/b + 1/c is an integer.
