## Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  296.10008
Autor:  Erdös, Paul; Graham, Ronald L.; Ruzsa, I.Z.; Straus, E.G.
Title:  On the prime factors of \binom{2n}{n}. (In English)
Source:  Math. Comput. 29, 83-92 (1975).
Review:  The present paper is devoted to a quantitative study of the factors of the binomial coefficient Bn = \binom{2n}{n}. Among the results obtained are the following: (1) for any two odd primes p and q, (Bn,pq) = 1 for infinitely many integers n; (2) if f(n) = sum 1/p where the summation is over all primes p such that p \leq n and p \nmid Bn, then limx ––> oox-1 sum xn = 1f(n) = sum ook = 2 log k/2k; (3) if p is a fixed prime and

S = {n \leq x: p\alpha |Bn and p\alpha \not in (n ½- \epsilon,n ½+\epsilon)},

then the cardinality of S is 0(x).
Reviewer:  P.Hagis jun.
Classif.:  * 11B39 Special numbers, etc.
11A41 Elemementary prime number theory
05A10 Combinatorial functions

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