2015 IMO Problems/Problem 5

Let $\mathbb{R}$ be the set of real numbers. Determine all functions $f$ : $\mathbb{R}\rightarrow\mathbb{R}$ satisfying the equation

$f(x+f(x+y))+f(xy) = x+f(x+y)+yf(x)$

for all real numbers $x$ and $y$ .

Proposed by Dorlir Ahmeti, Albania

This problem needs a solution. If you have a solution for it, please help us out by adding it.

Page