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: 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.

**[1]**P. Erdős, "Über die Anzahl der Primfaktoren von ,"*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 ,"*Math. Comp.*, v. 29, 1975, pp. 83-92.**[4]**P. Erdős, H. Gupta & S. P. Khare, "On the number of distinct prime divisors of ,"*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)**

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DOI:
https://doi.org/10.1090/S0025-5718-1988-0942159-6

Article copyright:
© Copyright 1988
American Mathematical Society