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International Journal of Mathematics and Mathematical Sciences
Volume 22, Issue 2, Pages 431-435

A short proof of an identity of Sylvester

Department of Mathematics, The Ohio State University, Columbus 43210, OH, USA

Received 16 October 1996

Copyright © 1999 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We present two short proofs of an identity found by Sylvester and rediscovered by Louck. The first proof is an elementary version of Knuth's proof and is analogous to Macdonald's proof of a related identity of Milne. The second is Sylvester's own proof of his identity.