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|a_i -a_j| all different

Source: 2005 Cuba MO 2.6

September 15, 2024
algebrainequalities

Problem Statement

All positive differences aiaja_i -a_j of five different positive integers a1a_1, a2a_2, a3a_3, a4a_4 and a5a_5 are all different. Let AA be the set formed by the largest elements of each group of 55 elements that meet said condition. Determine the minimum element of AA.