VN-TST 2016 Problem 1

Find all $a,n\in\mathbb{Z}^+$ ( $a>2$ ) such that each prime divisor of $a^n-1$ is also prime divisor of $a^{3^{2016}}-1$

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.