FI-MO 2012 Problem 3

Prove that for all integers $k\geq 2,$ the number $k^{k-1}-1$ is divisible by $(k-1)^2.$

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.