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all terms of the sequence are equal.

Source: Polish MO Second Round 1974 p6

September 8, 2024
algebracombinatorics

Problem Statement

There is a sequence of integers a1,a2,,a2n+1 a_1, a_2, \ldots, a_{2n+1} with the following property: after eliminating any term, the remaining ones can be divided into two groups of n n terms such that the sum of the terms in the first group is equal to the sum words in the second. Prove that all terms of the sequence are equal.