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Good permutations

Source: Iranian TST 2015 second exam p5

June 5, 2015
number theorycombinatorics

Problem Statement

We call a permutation (a1,a2,⋯ ,an)(a_1, a_2,\cdots , a_n) of the set {1,2,⋯ ,n}\{ 1,2,\cdots, n\} "good" if for any three natural numbers i<j<ki <j <k, n∤ai+ak−2ajn\nmid a_i+a_k-2a_j find all natural numbers n≥3n\ge 3 such that there exist a "good" permutation of a set {1,2,⋯ ,n}\{1,2,\cdots, n\}.
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