VN-TST 1990 Problem 3

Prove that there is no real function $f(x)$ satisfying $f\left(f(x)\right) = x^2 - 2$ for all real number $x$ .

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.