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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Infinite covering systems of congruences
which don't exist


Author: Ethan Lewis
Journal: Proc. Amer. Math. Soc. 124 (1996), 355-360
MSC (1991): Primary 11B25; Secondary 11A07
MathSciNet review: 1301513
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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

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03088-2
PII: S 0002-9939(96)03088-2
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
Article copyright: © Copyright 1996 American Mathematical Society