TH-TMO 2015 Problem 5

Let $n$ be an integer greater than $6$ .Show that if $n+1$ is a prime number,than $\left\lceil \frac{(n-1)!}{n(n+1)}\right \rceil$ is $ODD.$

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.