IMO 2017 Shortlist A5
An integer n ě 3 is given. We all an n-tuple of real numbers px1,x2,...,xnq Shiny if for ea h permutation y1,y2,...,yn o...
Category: Algebra
Problem
An integer n ě 3 is given. We all an n-tuple of real numbers px1,x2,...,xnq Shiny
if for ea h permutation y1,y2,...,yn of these numbers we have
n´1 ÿ
i“1
yiyi1 “ y1y2 y2y3 y3y4 ¨¨¨ ` yn´1yn ě ´1.
Find the largest onstant K “ Kpnq su h that
ÿ
1ďiăjďn
xixj ě K
holds for every Shiny n-tuple px1,x2,...,xnq.
(Serbia)