PAMO 2018 Problem 1

Find all functions $f : \mathbb Z \to \mathbb Z$ such that $(f(x + y))^2 = f(x^2) + f(y^2)$ for all $x, y \in \mathbb Z$ .

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.