Infinite covering systems of congruences which don’t exist

Lewis, Ethan

doi:10.1090/S0002-9939-96-03088-2

Infinite covering systems of congruences which don’t exist
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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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