IMO 2021 Shortlist A7

Let n ě 1 be an integer, and let x0,x1,...,xn1 be n 2 non-negative real numbers that satisfy xixi1 ´x2 i´1 ě1 for all i ...

IMO 2021 Shortlist A7

Category: Algebra

Problem

Let n ě 1 be an integer, and let x0,x1,...,xn1 be n 2 non-negative real numbers that satisfy xixi1 ´x2 i´1 ě1 for all i “1,2,...,n. Show that x0 x1 ¨¨¨xn xn1 ą ˆ 2n ˙3{2 .