IMO 2016 Shortlist A3
Find all integers n ⩾ 3 with the following property: for all real numbers a1,a2,...,an and b1,b2,...,bn satisfying |ak| ...
Category: Algebra
Problem
Find all integers n ⩾ 3 with the following property: for all real numbers a1,a2,...,an and b1,b2,...,bn satisfying |ak| + |bk| = 1 for 1 ⩽ k ⩽ n, there exist x1,x2,...,xn, each of which is either −1 or 1, such that n X k=1 xkak + n X k=1 xkbk ⩽ 1.