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

marked as duplicate by Andrey Rekalo, Martin Brandenburg, Qiaochu Yuan, Pete L. Clark, Andy Putman Mar 31 '11 at 1:54This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question. 


You can look at M.D. Choi's paper http://www.jstor.org/stable/pdfplus/2975779.pdf (American Math Monthly, 1983, "Tricks or Treats with the Hilbert Matrix") for this, and much more. 


Look at the paper below for what you are asking and much more! There is a lot known about the Hilbert matrix.


