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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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The minimal number of solutions to $\phi (n)=\phi (n+k)$
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by Jeffrey J. Holt;
Math. Comp. 72 (2003), 2059-2061
DOI: https://doi.org/10.1090/S0025-5718-03-01509-6
Published electronically: February 3, 2003

Abstract:

In 1958, A. Schinzel showed that for each fixed $k\leq 8\cdot 10^{47}$ there are at least two solutions to $\phi (n)=\phi (n+k)$. Using the same method and a computer search, Schinzel and A. Wakulicz extended the bound to all $k \leq 2\cdot 10^{58}$. Here we show that Schinzel’s method can be used to further extend the bound when $k$ is even, but not when $k$ is odd.
References
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Bibliographic Information
  • Jeffrey J. Holt
  • Affiliation: Department of Mathematics, Randolph-Macon College, Ashland, Virginia 23005
  • Address at time of publication: Department of Mathematics, University of Virginia, Charlottesville, Virginia 22904
  • Email: jjholt@virginia.edu
  • Received by editor(s): August 14, 1998
  • Received by editor(s) in revised form: March 5, 2002
  • Published electronically: February 3, 2003
  • Additional Notes: The author was partially supported by a grant from the Walter Williams Craigie Endowment.
  • © Copyright 2003 American Mathematical Society
  • Journal: Math. Comp. 72 (2003), 2059-2061
  • MSC (2000): Primary 11N25; Secondary 11Y99
  • DOI: https://doi.org/10.1090/S0025-5718-03-01509-6
  • MathSciNet review: 1986821