IMO 2014 Shortlist A1

Let z0 ă z1 ă z2 ă ¨¨¨ be an infinite sequence of positive integers. Prove that there exists a unique integer n ě 1 such...

imomathematicsolympiadshortlistalgebra

IMO 2014 Shortlist A1

Category: Algebra

Problem

Let z0 ă z1 ă z2 ă ¨¨¨ be an infinite sequence of positive integers. Prove that there exists a unique integer n ě 1 such that zn ă z0 z1 ¨¨¨ zn n ď zn1. (Austria)