Y by abk2015, Davi-8191, integrated_JRC, itslumi, MathLuis, centslordm, guillermo.dinamarca, HWenslawski, GeoKing, Adventure10, Mathefishian, bjump, ItsBesi, and 1 other user
Determine all positive integers
for which
is an integer. Here
denotes the greatest integer less than or equal to
.

![$\dfrac{n^2+1}{[\sqrt{n}]^2+2}$](http://latex.artofproblemsolving.com/7/e/d/7ed6c67114c0c7d262f67e5b7a733daab7997415.png)
![$[r]$](http://latex.artofproblemsolving.com/2/f/c/2fcabe2c2b8ebe2c428830acb9874cb8a8df790f.png)
