> **Possible Duplicate:**  
> [Deriving Inverse of Hilbert Matrix](https://mathoverflow.net/questions/47561/deriving-inverse-of-hilbert-matrix)  


The inverse of the [Hilbert Matrix][1] is made up entirely of integer entries, but I can't seem to
find an elementary proof for that though, any hints?


  [1]: http://en.wikipedia.org/wiki/Hilbert_matrix