IMO 2018 Shortlist A4

Let a0,a1,a2,... be a sequen e of real numbers su h that a0 “ 0, a1 “ 1, and for every n ě 2 there exists 1 ď k ď n sati...

IMO 2018 Shortlist A4

Category: Algebra

Problem

Let a0,a1,a2,... be a sequen e of real numbers su h that a0 “ 0, a1 “ 1, and for every n ě 2 there exists 1 ď k ď n satisfying an “ an´1 ¨¨¨ an´k k . Find the maximal possible value of a2018 ´ a2017. (Belgium)