MathDB

11

Part of 1996 Baltic Way

Problems(1)

At least three of x_i are equal

Source: Baltic Way 1996 Q11

3/19/2011
Real numbers x1,x2,…,x1996x_1,x_2,\ldots ,x_{1996} have the following property: For any polynomial WW of degree 22 at least three of the numbers W(x1),W(x2),…,W(x1996)W(x_1),W(x_2),\ldots ,W(x_{1996}) are equal. Prove that at least three of the numbers x1,x2,…,x1996x_1,x_2,\ldots ,x_{1996} are equal.
algebrapolynomialalgebra proposed