Find all positive integers n such that $n\mid\lfloor(n-1)!/(n+1)\rfloor$

Question

Find all positive integers $n$ such that $n\ \big|\ \left\lfloor\frac{(n-1)!}{n+1}\right\rfloor$.

The answer says that when $n<5$, the condition holds for $n=1$ only. But I think $n=2,3$ also hold.

Which is correct?

Answer 1

You are right, $n$ divides $0$ for every integer $n$.