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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2024 MCQ for Mathematics of Computation is 1.78.

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A new function associated with the prime factors of $(^{n}_{k})$
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by E. F. Ecklund, P. Erdös and J. L. Selfridge PDF
Math. Comp. 28 (1974), 647-649 Request permission

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
  • E. F. Ecklund Jr., On prime divisors of the binomial coefficient, Pacific J. Math. 29 (1969), 267–270. MR 244148, DOI 10.2140/pjm.1969.29.267
    • P. Erdös, "Some problems in number theory," in Computers in Number Theory, Academic Press, London, 1971, pp. 405-414.
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Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Math. Comp. 28 (1974), 647-649
  • MSC: Primary 10A20
  • DOI: https://doi.org/10.1090/S0025-5718-1974-0337732-2
  • MathSciNet review: 0337732