OIM 2022 Problem 6

Find all functions $f:\mathbb{N} \rightarrow \mathbb{N}$ , such that $f(a)f(a+b)-ab$ is a perfect square for all $a, b \in \mathbb{N}$ .

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.