MathDB
IMAR Test 2018 P2

Source: IMAR Test 2018 P2

April 21, 2021
algebrapolynomialminimum valuepermutationromania

Problem Statement

Let PP be a non-zero polynomial with non-negative real coefficients, let NN be a positive integer, and let σ\sigma be a permutation of the set {1,2,...,n}\{1,2,...,n\}. Determine the least value the sum ∑i=1nP(xi2)P(xixσ(i))\sum_{i=1}^{n}\frac{P(x_i^2)}{P(x_ix_{\sigma(i)})} may achieve, as x1,x2,...,xnx_1,x_2,...,x_n run through the set of positive real numbers.
Fedor Petrov
Back to ProblemsView on AoPS