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Function difference is a polynomial

Source: 2012 Indonesia Round 2 TST 4 Problem 1

March 18, 2012

functionalgebrapolynomialinductionalgebra unsolved

Problem Statement

Let

P

be a polynomial with real coefficients. Find all functions

f : \mathbb{R} \rightarrow \mathbb{R}

such that there exists a real number

t

such that

f(x+t) - f(x) = P(x)

for all

x \in \mathbb{R}