Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



On prime divisors of binomial coefficients

Author: Pierre Goetgheluck
Journal: Math. Comp. 51 (1988), 325-329
MSC: Primary 11B65; Secondary 11A51, 11Y05
MathSciNet review: 942159
Full-text PDF

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.

References [Enhancements On Off] (What's this?)

  • [1] 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.
  • [2] P. Erdős, "Some unconventional problems in number theory," Acta Math. Acad. Sci. Hungar., v. 33, 1979, pp. 71-80. MR 515121 (80b:10001)
  • [3] 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. 83-92.
  • [4] 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. 51-60.
  • [5] P. Goetgheluck, "Computing binomial coefficients," Amer. Math. Monthly, v. 94, 1987, pp. 360-365. MR 1541073
  • [6] P. A. B. Pleasants, "The number of prime factors of binomial coefficients," J. Number Theory, v. 15, 1982, pp. 203-225. MR 675185 (84a:10007)
  • [7] A. Sárközy, "On divisors of binomial coefficients, I," J. Number Theory, v. 20, 1985, pp. 70-80. MR 777971 (86c:11002)

Similar Articles

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

American Mathematical Society