MEMO 2007 T4

Find all positive integers $k$ with the following property: There exists an integer $a$ so that $(a+k)^{3}-a^{3}$ is a multiple of $2007$ .

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.