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Permutations of 1, 2, ..., 2n with equality condition

Source: IV Caucasus Mathematic Olympiad

April 7, 2019
algebrapermutations

Problem Statement

Find all positive integers n⩾2n\geqslant 2 such that there exists a permutation a1a_1, a2a_2, a3a_3, \ldots, a2na_{2n} of the numbers 1,2,3,…,2n1, 2, 3, \ldots, 2n satisfying a1⋅a2+a3⋅a4+…+a2n−3⋅a2n−2=a2n−1⋅a2n.a_1\cdot a_2 + a_3\cdot a_4 + \ldots + a_{2n-3} \cdot a_{2n-2} = a_{2n-1} \cdot a_{2n}.
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