UZ-MO 2011 Problem 4

Does existes a function $f:N->N$ and for all positeve integer n $f(f(n)+2011)=f(n)+f(f(n))$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.