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Find the Polynomial

Source: ToT - 2001 Spring Senior A-Level #1

August 17, 2011
algebrapolynomialalgebra unsolved

Problem Statement

Find at least one polynomial P(x)P(x) of degree 2001 such that P(x)+P(1āˆ’x)=1P(x)+P(1- x)=1 holds for all real numbers xx.