MathDB

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Part of 1983 IMO Longlists

Problems(1)

Inequality on k variables

Source:

10/7/2010
Given positive integers k,m,nk,m, n with km≤nkm \leq n and non-negative real numbers x1,…,xkx_1, \ldots , x_k, prove that n(∏i=1kxim−1)≤m∑i=1k(xin−1).n \left( \prod_{i=1}^k x_i^m -1 \right) \leq m \sum_{i=1}^k (x_i^n-1).
inequalitiesinequalities proposed