MathDB
Inequality

Source: Baltic way 2009

November 11, 2009
inequalitiesalgebrapolynomialinequalities proposed

Problem Statement

Let a1,a2,…,a100 a_1,a_{2},\ldots ,a_{100} be nonnegative integers satisfying the inequality a1⋅(a1−1)⋅…⋅(a1−20)+a2⋅(a2−1)⋅…⋅(a2−20)+…+a100⋅(a100−1)⋅…⋅(a100−20)≤100⋅99⋅98⋅…⋅79.a_1\cdot (a_1-1)\cdot\ldots\cdot (a_1-20)+a_2\cdot (a_2-1)\cdot\ldots\cdot (a_2-20)+\\ \ldots+a_{100}\cdot (a_{100}-1)\cdot\ldots\cdot (a_{100}-20)\le 100\cdot 99\cdot 98\cdot\ldots\cdot 79. Prove that a1+a2+…+a100≤9900a_1+a_2+\ldots+a_{100}\le 9900.
Back to ProblemsView on AoPS