Find the positive integers $n$ with $n \geq 4$ such that $[\sqrt{n}]+1$ divides $n-1$ and $[\sqrt{n}]-1$ divides $n+1$.
HIDE: Remark This problem can be solved in a similar way with the one given at Cono Sur Olympiad 2006, problem 5.Problem
Source: Romanian JBTST II 2007, problem 1
Tags: function, geometry, 3D geometry, number theory proposed, number theory