IMO 2007 Shortlist A3

Let n be a positive integer, and let x and y be positive real numbers such that xn +yn = 1. Prove that n X k=1 1 + x2k 1...

imomathematicsolympiadshortlistalgebra

IMO 2007 Shortlist A3

Category: Algebra

Problem

Let n be a positive integer, and let x and y be positive real numbers such that xn +yn = 1. Prove that n X k=1 1 + x2k 1 + x4k ! n X k=1 1 + y2k 1 + y4k ! < (1 − x)(1 − y) . (Estonia)