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Proceedings of the American Mathematical Society

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

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Infinite covering systems of congruences which don’t exist
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by Ethan Lewis PDF
Proc. Amer. Math. Soc. 124 (1996), 355-360 Request permission

Abstract:

We prove there is no infinite set of congruences with: every integer satisfying exactly one congruence, distinct moduli, the sum of the reciprocals of the moduli equal to 1, the lcm of the moduli divisible by only finitely many primes, and a prime greater than 3 dividing any of the moduli.
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Additional Information
  • Ethan Lewis
  • Affiliation: Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6395
  • Email: ethan@thales.math.upenn.edu
  • Received by editor(s): December 9, 1992
  • Received by editor(s) in revised form: April 18, 1994, and August 20, 1994
  • Additional Notes: Supported in part by DOE grant P200A20337.
  • Communicated by: William W. Adams
  • © Copyright 1996 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 124 (1996), 355-360
  • MSC (1991): Primary 11B25; Secondary 11A07
  • DOI: https://doi.org/10.1090/S0002-9939-96-03088-2
  • MathSciNet review: 1301513