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**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 B_{n} = \binom{2n}{n}. Among the results obtained are the following: (1) for any two odd primes p and q, (B_{n},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 B_{n}, then **lim**_{x ––> oo}x^{-1} **sum** ^{x}_{n = 1}f(n) = **sum** ^{oo}_{k = 2} log k/2^{k}; (3) if p is a fixed prime and S = **{**n \leq x: p^{\alpha} |B_{n} 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

© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag