MathDB

Prove that all x_i are equal

Source: Baltic Way 2011

November 6, 2011

algebra proposedalgebra

Problem Statement

The real numbers

x_1,\ldots ,x_{2011}

satisfy

x_1+x_2=2x_1',\ x_2+x_3=2x_2', \ \ldots, \ x_{2011}+x_1=2x_{2011}'

where

x_1',x_2',\ldots,x_{2011}'

is a permutation of

x_1,x_2,\ldots,x_{2011}

. Prove that

x_1=x_2=\ldots =x_{2011}