On prime divisors of binomial coefficients
Author:
Pierre Goetgheluck
Journal:
Math. Comp. 51 (1988), 325-329
MSC:
Primary 11B65; Secondary 11A51, 11Y05
DOI:
https://doi.org/10.1090/S0025-5718-1988-0942159-6
MathSciNet review:
942159
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Abstract | References | Similar Articles | Additional Information
Abstract: This paper, using computational and theoretical methods, deals with prime divisors of binomial coefficients: Geometric distribution and number of distinct prime divisors are studied. We give a numerical result on a conjecture by Erdős on square divisors of binomial coefficients.
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P. Erdős, "Über die Anzahl der Primfaktoren von $\left ( {\begin {array}{*{20}{c}} n \\ k \\ \end {array} } \right )$," Arch. Math., v. 24, 1973, pp. 53-56.
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- P. Goetgheluck, Notes: Computing Binomial Coefficients, Amer. Math. Monthly 94 (1987), no. 4, 360–365. MR 1541073, DOI https://doi.org/10.2307/2323099
- P. A. B. Pleasants, The number of prime factors of binomial coefficients, J. Number Theory 15 (1982), no. 2, 203–225. MR 675185, DOI https://doi.org/10.1016/0022-314X%2882%2990026-9
- A. Sárközy, On divisors of binomial coefficients. I, J. Number Theory 20 (1985), no. 1, 70–80. MR 777971, DOI https://doi.org/10.1016/0022-314X%2885%2990017-4
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Article copyright:
© Copyright 1988
American Mathematical Society