IMO 2022 Shortlist A4
Let n ě 3 be an integer, and let x1,x2,...,xn be real numbers in the interval r0,1s. Let s “ x1 x2 ...xn, and assume tha...
Category: Algebra
Problem
Let n ě 3 be an integer, and let x1,x2,...,xn be real numbers in the interval r0,1s.
Let s “ x1 x2 ...`xn, and assume that s ě 3. Prove that there exist integers i and j with
1 ď i ă j ď n such that
2j´i
xixj ą 2s´3
.
(Trinidad and Tobago)