MEMO 2022 I1

Find all functions $f: \mathbb R \to \mathbb R$ such that $f(x+f(x+y))=x+f(f(x)+y)$ holds for all real numbers $x$ 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.