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Let

p

and

q

be prime numbers with

p<q

. Suppose that in a convex polygon

P_1,P_2,…,P_{pq}

all angles are equal and the side lengths are distinct positive integers. Prove that

P_1P_2+P_2P_3+\cdots +P_kP_{k+1}\geqslant \frac{k^3+k}{2}

holds for every integer

k

with

1\leqslant k\leqslant p

.
Proposed by Ander Lamaison Vidarte, Berlin Mathematical School, Berlin

Problem Statement