On prime divisors of binomial coefficients
Author:
Pierre Goetgheluck
Journal:
Math. Comp. 51 (1988), 325329
MSC:
Primary 11B65; Secondary 11A51, 11Y05
MathSciNet review:
942159
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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 ," Arch. Math., v. 24, 1973, pp. 5356.
 [2]
 P. Erdős, "Some unconventional problems in number theory," Acta Math. Acad. Sci. Hungar., v. 33, 1979, pp. 7180. MR 515121 (80b:10001)
 [3]
 P. Erdős, R. L. Graham, I. Ruzsa & E. G. Straus, "On the prime factors of ," Math. Comp., v. 29, 1975, pp. 8392.
 [4]
 P. Erdős, H. Gupta & S. P. Khare, "On the number of distinct prime divisors of ," Utilitas Math., v. 10, 1976, pp. 5160.
 [5]
 P. Goetgheluck, "Computing binomial coefficients," Amer. Math. Monthly, v. 94, 1987, pp. 360365. MR 1541073
 [6]
 P. A. B. Pleasants, "The number of prime factors of binomial coefficients," J. Number Theory, v. 15, 1982, pp. 203225. MR 675185 (84a:10007)
 [7]
 A. Sárközy, "On divisors of binomial coefficients, I," J. Number Theory, v. 20, 1985, pp. 7080. MR 777971 (86c:11002)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198809421596
PII:
S 00255718(1988)09421596
Article copyright:
© Copyright 1988
American Mathematical Society
