KöMaL 2017 B4895

Prove that if $n-1$ and $n+1$ are both primes and $n> 6$ is an integer then $n^2(n^2+16)$ is divisible by 720.

Official text KöMaL. 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.