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China Team Selection Test 2014 TST 3 Day 2 Q5

Source: China Nanjing , 24 Mar 2014

March 24, 2014
complex numbersinequalities proposedinequalitiesChina TST

Problem Statement

Let nn be a given integer which is greater than 11 . Find the greatest constant λ(n)\lambda(n) such that for any non-zero complex z1,z2,⋯ ,znz_1,z_2,\cdots,z_n ,have that \sum_{k\equal{}1}^n |z_k|^2\geq \lambda(n)\min\limits_{1\le k\le n}\{|z_{k+1}-z_k|^2\}, where zn+1=z1z_{n+1}=z_1.
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