PAMO 2010 Problem 6

Does there exist a function $f:\mathbb{Z}\to\mathbb{Z}$ such that $f(x+f(y))=f(x)-y$ for all integers $x$ and $y$ ?

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.