CGMO 2012 Problem 8

Find the number of integers $k$ in the set $\{0, 1, 2, \dots, 2012\}$ such that $\binom{2012}{k}$ is a multiple of $2012$ .

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.