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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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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