Problem

Source: ELMO Shortlist 2013: Problem A3, by Calvin Deng

Tags: algebra, polynomial, functional equation



Find all $f:\mathbb{R}\to\mathbb{R}$ such that for all $x,y\in\mathbb{R}$, $f(x)+f(y) = f(x+y)$ and $f(x^{2013}) = f(x)^{2013}$. Proposed by Calvin Deng