IMO 2015 Shortlist A3

Let n be a fixed positive integer. Find the maximum possible value of ÿ 1ďrăsď2n ps ´ r ´ nqxrxs , where ´1 ď xi ď 1 for...

imomathematicsolympiadshortlistalgebra

IMO 2015 Shortlist A3

Category: Algebra

Problem

Let n be a fixed positive integer. Find the maximum possible value of ÿ 1ďrăsď2n ps ´ r ´ nqxrxs , where ´1 ď xi ď 1 for all i “ 1,2,...,2n. (Austria)