On the prime factors of (²ⁿ_{𝑛})

Author:

Erdős P.,Graham R. L.,Ruzsa I. Z.,Straus E. G.

Abstract

Several quantitative results are given expressing the fact that ( n 2 n ) (_n^{2n}) is usually divisible by a high power of the small primes. On the other hand, it is shown that for any two primes p and q, there exist infinitely many n for which ( ( n 2 n ) , p q ) = 1 ((_n^{2n}),pq) = 1 .

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Reference3 articles.

1. H. BALAKRAN, "On the values of n which make (2𝑛)!/(𝑛+1)!(𝑛+1)! an integer," J. Indian Math. Soc., v. 18, 1929, pp. 97-100.

2. On some divisibility properties of 2𝑛\choose𝑛;Erdős, P.;Canad. Math. Bull.,1964

3. P. ERDÖS, "Aufgabe 557," Elemente Math., v. 23, 1968, pp. 111-113.

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Fractal projections with an application in number theory;Ergodic Theory and Dynamical Systems;2022-03-16

2. On prime divisors of binomial coefficients;Mathematics of Computation;1988

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