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Published in:
2004 | OriginalPaper | Chapter
Binomial coefficients are (almost) never powers
Authors : Martin Aigner, Günter M. Ziegler
Published in: Proofs from THE BOOK
Publisher: Springer Berlin Heidelberg
Included in: Professional Book Archive
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There is an epilogue to Bertrand’s postulate which leads to a beautiful result on binomial coefficients. In 1892 Sylvester strengthened Bertrand’s postulate in the following way: $$In\;n > 2k,then\;at\;least\;one\;of\;the\;numbers\;n,n - 1,...,n - k + 1\;has\;a\;prime\;divisor\;p\;greater\;than\;k.$$.