IMO 2010 Shortlist A7

Let a1,...,ar be positive real numbers. For n ¡r, we inductively define an  max 1¨k¨n1 pak ankq. (1) Prove that there...

imomathematicsolympiadshortlistalgebra

IMO 2010 Shortlist A7

Category: Algebra

Problem

Let a1,...,ar be positive real numbers. For n ¡r, we inductively define an  max 1¨k¨n1 pak ankq. (1) Prove that there exist positive integers ℓ ¨r and N such that an anℓ aℓ for all n ©N. (Iran)