On prime divisors of binomial coefficients
Author:
Pierre Goetgheluck
Journal:
Math. Comp. 51 (1988), 325329
MSC:
Primary 11B65; Secondary 11A51, 11Y05
DOI:
https://doi.org/10.1090/S00255718198809421596
MathSciNet review:
942159
Fulltext PDF Free Access
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.

P. Erdős, "Über die Anzahl der Primfaktoren von $\left ( {\begin {array}{*{20}{c}} n \\ k \\ \end {array} } \right )$," Arch. Math., v. 24, 1973, pp. 5356.
 P. Erdős, Some unconventional problems in number theory, Acta Math. Acad. Sci. Hungar. 33 (1979), no. 12, 71–80. MR 515121, DOI https://doi.org/10.1007/BF01903382 P. Erdős, R. L. Graham, I. Ruzsa & E. G. Straus, "On the prime factors of $\left ( {\begin {array}{*{20}{c}} {2n} \\ n \\ \end {array} } \right )$," Math. Comp., v. 29, 1975, pp. 8392. P. Erdős, H. Gupta & S. P. Khare, "On the number of distinct prime divisors of $\left ( {\begin {array}{*{20}{c}} n \\ k \\ \end {array} } \right )$," Utilitas Math., v. 10, 1976, pp. 5160.
 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/10.1016/0022314X%2882%29900269
 A. Sárközy, On divisors of binomial coefficients. I, J. Number Theory 20 (1985), no. 1, 70–80. MR 777971, DOI https://doi.org/10.1016/0022314X%2885%29900174
Retrieve articles in Mathematics of Computation with MSC: 11B65, 11A51, 11Y05
Retrieve articles in all journals with MSC: 11B65, 11A51, 11Y05
Additional Information
Article copyright:
© Copyright 1988
American Mathematical Society