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find the least k

Source: 2009 China Western Mathematic Olmpiad

February 25, 2012
combinatorics proposedcombinatorics

Problem Statement

Given an integer n≥ 3n\ge\ 3, find the least positive integer kk, such that there exists a set AA with kk elements, and nn distinct reals x1,x2,…,xnx_{1},x_{2},\ldots,x_{n} such that x1+x2,x2+x3,…,xn−1+xn,xn+x1x_{1}+x_{2}, x_{2}+x_{3},\ldots, x_{n-1}+x_{n}, x_{n}+x_{1} all belong to AA.
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