Question 4
Find all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ satisfying the equation
$$
f(x+f(x+y))+f(x y)=x+f(x+y)+y f(x)
$$
for all real numbers $x$ and $y$.
$$
f(x+f(x+y))+f(x y)=x+f(x+y)+y f(x)
$$
for all real numbers $x$ and $y$.
IMO 2015 — Complete Shortlist Question 4
IMO Shortlist · IMO 2015 — Complete Shortlist