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International Mathematics Competition
for University Students
2018

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IMC 2025
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IMC2018: Day 1, Problem 5

Problem 5. Let p and q be prime numbers with p<q. Suppose that in a convex polygon P1P2Ppq all angles are equal and the side lengths are distinct positive integers. Prove that

P1P2+P2P3++PkPk+1k3+k2

holds for every integer k with 1kp.

(Proposed by Ander Lamaison Vidarte, Berlin Mathematical School, Berlin)

        

IMC
2018

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