ZA-SAMO 2012 Problem 6

Find all functions $f:\mathbb{N}\to\mathbb{R}$ such that $f(km)+f(kn)-f(k)f(mn)\ge 1$ for all $k,m,n\in\mathbb{N}$ .

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.