Claims

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1934_10_01_erdos: Erdős's 1934 proof of the Sylvester-Schur theorem: for n at least 2k the binomial coefficient n choose k has a prime factor greater than k; refereed in J. London Math. Soc., and by symmetry it settles n/2 <= k <= n-1.

1955_01_01_erdos: Theorem 1 of Erdős's 1955 paper on consecutive integers: any c_1 k / log k consecutive integers above k include one with a prime factor greater than k; refereed in Nieuw Arch. Wisk., it gives P(n choose k) >> min(n-k+1, k log k).

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