CMOQR 2016 Problem 4

Determine all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ such that $f(x + f(y)) + f(x - f(y)) = x.$

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.