MathDB
Inequality

Source: Vietnam NMO 1987 Problem 4

February 4, 2009
inequalitiesinequalities unsolved

Problem Statement

Let a1 a_1, a2 a_2, … \ldots, an a_n be positive real numbers (n≥2 n \ge 2) whose sum is S S. Show that \sum_{i\equal{}1}^n\frac{a_i^{2^{k}}}{\left(S\minus{}a_i\right)^{2^t\minus{}1}}\ge\frac{S^{1\plus{}2^k\minus{}2^t}}{\left(n\minus{}1\right)^{2^t\minus{}1}n^{2^k\minus{}2^t}} for any nonnegative integers k k, t t with k≥t k \ge t. When does equality occur?
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