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Mathematics of Computation

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A new function associated with the prime factors of $(^{n}_{k})$


Authors: E. F. Ecklund, P. Erdös and J. L. Selfridge
Journal: Math. Comp. 28 (1974), 647-649
MSC: Primary 10A20
DOI: https://doi.org/10.1090/S0025-5718-1974-0337732-2
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?)

  • E. F. Ecklund Jr., On prime divisors of the binomial coefficient, Pacific J. Math. 29 (1969), 267–270. MR 244148
  • 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