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On the prime factors of $ (\sp{2n}\sb{n})$

Authors: P. Erdős, R. L. Graham, I. Z. Ruzsa and E. G. Straus
Journal: Math. Comp. 29 (1975), 83-92
MSC: Primary 10H15; Secondary 10L10
MathSciNet review: 0369288
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Abstract: Several quantitative results are given expressing the fact that $ (_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^{2n}),pq) = 1$.

References [Enhancements On Off] (What's this?)

  • [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] P. Erdős, On some divisibility properties of 2𝑛\choose𝑛, Canad. Math. Bull. 7 (1964), 513–518. MR 169809,
  • [3] P. ERDÖS, "Aufgabe 557," Elemente Math., v. 23, 1968, pp. 111-113.

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Article copyright: © Copyright 1975 American Mathematical Society