Binomial coefficients are (almost) never powers
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:
If n ≥ 2k, then at least one of the numbers n, n − 1,..., n − k + 1 has a prime divisor p greater than k.
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- J. J. Sylvester: On arithmetical series, Messenger of Math. 21 (1892), 1–19 87-120; Collected Mathematical Papers Vol. 4, 1912, 687-731.Google Scholar
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