PAMO 2009 Problem 5

Find all functions $f:\mathbb{N}_0\to\mathbb{N}_0$ for which $f(0)=0$ and $f(x^2-y^2)=f(x)f(y)$ for all $x,y\in\mathbb{N}_0$ with $x>y$ .

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.