Problem

Source: 2012 Indonesia Round 2 TST 4 Problem 1

Tags: function, algebra, polynomial, induction, algebra unsolved



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 $x \in \mathbb{R}$.