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.**33**(1979), no. 1-2, 71–80. Special issue dedicated to George Alexits on the occasion of his 80th birthday. MR**515121**, https://doi.org/10.1007/BF01903382**[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,*Notes: Computing Binomial Coefficients*, Amer. Math. Monthly**94**(1987), no. 4, 360–365. MR**1541073**, https://doi.org/10.2307/2323099**[6]**P. A. B. Pleasants,*The number of prime factors of binomial coefficients*, J. Number Theory**15**(1982), no. 2, 203–225. MR**675185**, https://doi.org/10.1016/0022-314X(82)90026-9**[7]**A. Sárközy,*On divisors of binomial coefficients. I*, J. Number Theory**20**(1985), no. 1, 70–80. MR**777971**, https://doi.org/10.1016/0022-314X(85)90017-4

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

Article copyright:
© Copyright 1988
American Mathematical Society