MathDB
Inequality with integer parts

Source: VJIMC 2018, Category II, Problem 2

April 14, 2018
inequalitiesfloor functionInteger Partalgebra

Problem Statement

Let nn be a positive integer and let a1≤a2≤⋯≤ana_1\le a_2 \le \dots \le a_n be real numbers such that a1+2a2+⋯+nan=0.a_1+2a_2+\dots+na_n=0. Prove that a1[x]+a2[2x]+⋯+an[nx]≥0a_1[x]+a_2[2x]+\dots+a_n[nx] \ge 0 for every real number xx. (Here [t][t] denotes the integer satisfying [t]≤t<[t]+1[t] \le t<[t]+1.)
Back to ProblemsView on AoPS