OSN 2009 Problem 1

Find all positive integers $n\in\{1,2,3,\ldots,2009\}$ such that $4n^6 + n^3 + 5$ is divisible by $7$ .

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.