SILK-ROAD 2013 Problem 3

Find all non-decreasing functions $f\,:\,\mathbb{N}\to\mathbb{N}$ , such that $f(f(m)f(n)+m)=f(mf(n))+f(m)$

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.