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Mathematics of Computation

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A new function associated with the prime factors of $ (\sp{n}\sb{k})$

Authors: E. F. Ecklund, P. Erdös and J. L. Selfridge
Journal: Math. Comp. 28 (1974), 647-649
MSC: Primary 10A20
MathSciNet review: 0337732
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Abstract: Let $ g(k)$ denote the least integer $ > k + 1$ so that all the prime factors of $ \left( {\begin{array}{*{20}{c}} {g(k)} \\ k \\ \end{array} } \right)$ are greater than k. The irregular behavior of $ g(k)$ is studied, obtaining the following bounds: $ {k^{1 + c}} < g(k) < \exp \,(k(1 + o(1))).$ Numerical values obtained for $ g(k)$ with $ k \leqq 52$ are listed.

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

  • [1] E. F. Ecklund Jr., On prime divisors of the binomial coefficient, Pacific J. Math. 29 (1969), 267–270. MR 0244148
  • [2] P. Erdös, "Some problems in number theory," in Computers in Number Theory, Academic Press, London, 1971, pp. 405-414.

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Article copyright: © Copyright 1974 American Mathematical Society

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