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IMC2018: Day 1, Problem 5Problem 5. Let p and q be prime numbers with p<q. Suppose that in a convex polygon P1P2…Ppq all angles are equal and the side lengths are distinct positive integers. Prove that P1P2+P2P3+⋯+PkPk+1≥k3+k2 holds for every integer k with 1≤k≤p. (Proposed by Ander Lamaison Vidarte, Berlin Mathematical School, Berlin) | |||||||||||
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