MathDB

At least three of x_i are equal

Source: Baltic Way 1996 Q11

March 19, 2011

algebrapolynomialalgebra proposed

Problem Statement

Real numbers

x_1,x_2,\ldots ,x_{1996}

have the following property: For any polynomial

W

of degree

2

at least three of the numbers

W(x_1),W(x_2),\ldots ,W(x_{1996})

are equal. Prove that at least three of the numbers

x_1,x_2,\ldots ,x_{1996}

are equal.