A Problem for Geoff Pilling

Number Theory Level 3

True or false:

$\overline{(n-1)(n-3)(n-2)(n-5)(n-4)}_n$ is divisible by $n+1$ , were $n \geq 5$

Clarification: The subscript means number base $n$ . The line above the number means that $(n-1)\ldots$ are digits of the number.