MathDB
muirhead strikes again

Source: Romanian IMO TST 2005 - day 5, problem 2

April 24, 2005
inequalitiesinequalities proposed

Problem Statement

Let n≥2n\geq 2 be an integer. Find the smallest real value ρ(n)\rho (n) such that for any xi>0x_i>0, i=1,2,…,ni=1,2,\ldots,n with x1x2⋯xn=1x_1 x_2 \cdots x_n = 1, the inequality ∑i=1n1xi≤∑i=1nxir \sum_{i=1}^n \frac 1{x_i} \leq \sum_{i=1}^n x_i^r is true for all r≥ρ(n)r\geq \rho (n).
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